The susceptibilities in the spin-S Ising model
International Nuclear Information System (INIS)
Ainane, A.; Saber, M.
1995-08-01
The susceptibilities of the spin-S Ising model are evaluated using the effective field theory introduced by Tucker et al. for studying general spin-S Ising model. The susceptibilities are studied for all spin values from S = 1/2 to S = 5/2. (author). 12 refs, 4 figs
Transverse Ising spin-glass model
International Nuclear Information System (INIS)
Santos, Raimundo R. dos; Santos, R.M.Z. dos.
1984-01-01
The zero temperature behavior of the Transverse Ising spin-glass (+-J 0 ) model is discussed. The d-dimensional quantum model is shown to be equivalent to a classical (d + 1)- dimensional Ising spin-glass with correlated disorder. An exact Renormalization Group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin-glass in two-dimensions. (Author) [pt
Effective Hamiltonian for 2-dimensional arbitrary spin Ising model
International Nuclear Information System (INIS)
Sznajd, J.; Polska Akademia Nauk, Wroclaw. Inst. Niskich Temperatur i Badan Strukturalnych)
1983-08-01
The method of the reduction of the generalized arbitrary-spin 2-dimensional Ising model to spin-half Ising model is presented. The method is demonstrated in detail by calculating the effective interaction constants to the third order in cumulant expansion for the triangular spin-1 Ising model (the Blume-Emery-Griffiths model). (author)
Exact sampling hardness of Ising spin models
Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.
2017-09-01
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.
The spin S quantum Ising model at T=0
International Nuclear Information System (INIS)
Kamieniarz, G.; Kowalewski, L.; Piechocki, W.
1982-09-01
The Ising model with a transverse field for a general spin S is investigated within the framework of the Green-function method in the paramagnetic region at T=0. The analysis of selfconsistent equations gives a description of softmode phase transition as well as extrapolated values of critical fields and critical energy gap exponents. (author)
The transverse spin-1 Ising model with random interactions
Energy Technology Data Exchange (ETDEWEB)
Bouziane, Touria [Department of Physics, Faculty of Sciences, University of Moulay Ismail, B.P. 11201 Meknes (Morocco)], E-mail: touria582004@yahoo.fr; Saber, Mohammed [Department of Physics, Faculty of Sciences, University of Moulay Ismail, B.P. 11201 Meknes (Morocco); Dpto. Fisica Aplicada I, EUPDS (EUPDS), Plaza Europa, 1, San Sebastian 20018 (Spain)
2009-01-15
The phase diagrams of the transverse spin-1 Ising model with random interactions are investigated using a new technique in the effective field theory that employs a probability distribution within the framework of the single-site cluster theory based on the use of exact Ising spin identities. A model is adopted in which the nearest-neighbor exchange couplings are independent random variables distributed according to the law P(J{sub ij})=p{delta}(J{sub ij}-J)+(1-p){delta}(J{sub ij}-{alpha}J). General formulae, applicable to lattices with coordination number N, are given. Numerical results are presented for a simple cubic lattice. The possible reentrant phenomenon displayed by the system due to the competitive effects between exchange interactions occurs for the appropriate range of the parameter {alpha}.
Multi spin-flip dynamics: a solution of the one-dimensional Ising model
International Nuclear Information System (INIS)
Novak, I.
1990-01-01
The Glauber dynamics of interacting Ising spins (the single spin-flip dynamics) is generalized to p spin-flip dynamics with a simultaneous flip of up to p spins in a single configuration move. The p spin-flip dynamics is studied of the one-dimensional Ising model with uniform nearest-neighbour interaction. For this case, an exact relation is given for the time dependence of magnetization. It was found that the critical slowing down in this model could be avoided when p spin-flip dynamics with p>2 was considered. (author). 17 refs
Rigorous spin-spin correlation function of Ising model on a special kind of Sierpinski Carpets
International Nuclear Information System (INIS)
Yang, Z.R.
1993-10-01
We have exactly calculated the rigorous spin-spin correlation function of Ising model on a special kind of Sierpinski Carpets (SC's) by means of graph expansion and a combinatorial approach and investigated the asymptotic behaviour in the limit of long distance. The result show there is no long range correlation between spins at any finite temperature which indicates no existence of phase transition and thus finally confirms the conclusion produced by the renormalization group method and other physical arguments. (author). 7 refs, 6 figs
Quasi-realistic distribution of interaction fields leading to a variant of Ising spin glass model
International Nuclear Information System (INIS)
Tanasa, Radu; Enachescu, Cristian; Stancu, Alexandru; Linares, Jorge; Varret, Francois
2004-01-01
The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced
Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees
Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; Hofstad, Remco van der
2018-04-01
We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.
Mixed spin Ising model with four-spin interaction and random crystal field
International Nuclear Information System (INIS)
Benayad, N.; Ghliyem, M.
2012-01-01
The effects of fluctuations of the crystal field on the phase diagram of the mixed spin-1/2 and spin-1 Ising model with four-spin interactions are investigated within the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the two-dimensional square lattice. It has been found that the system exhibits a variety of interesting features resulting from the fluctuation of the crystal field interactions. In particular, for low mean value D of the crystal field, the critical temperature is not very sensitive to fluctuations and all transitions are of second order for any value of the four-spin interactions. But for relatively high D, the transition temperature depends on the fluctuation of the crystal field, and the system undergoes tricritical behaviour for any strength of the four-spin interactions. We have also found that the model may exhibit reentrance for appropriate values of the system parameters.
Stability and replica symmetry in the ising spin glass: a toy model
International Nuclear Information System (INIS)
De Dominicis, C.; Mottishaw, P.
1986-01-01
Searching for possible replica symmetric solutions in an Ising spin glass (in the tree approximation) we investigate a toy model whose bond distribution has two non vanishing cumulants (instead of one only as in a gaussian distribution)
Semi-local invariance in Ising models with multi-spin interaction
International Nuclear Information System (INIS)
Lipowski, A.
1996-08-01
We examine implications of semi-local invariance in Ising models with multispin interaction. In ergodic models all spin-spin correlation functions vanish and the local symmetry is the same as in locally gauge-invariant models. The d = 3 model with four-spin interaction is nonergodic at low temperature but the magnetic symmetry remains unbroken. The d = 3 model with eight-spin interaction is ergodic but undergoes the phase transition and most likely its low-temperature phase is characterized by a nonlocal order parameter. (author). 7 refs, 1 fig
International Nuclear Information System (INIS)
Vasconcelos Dos Santos, R.J.; Coutinho, S.
1995-01-01
The effect of a local field acting on decorating classical D-vector bond spins of an antiferromagnetic Ising model on the square lattice is studied for both the annealed isotropic and the axial decorated cases. In both models the effect on the phase diagrams of the transversal and the longitudinal components of the local field acting on the decorating spins are fully analyzed and discussed
The dilute spin-one Ising model with both bilinear and biquadratic exchange interactions
International Nuclear Information System (INIS)
Saber, M.
1987-08-01
The influence of bond and site dilution on the two-dimensional spin-one Ising model on a honeycomb lattice is investigated. Temperature-concentration phase diagrams for fixed values of the ratio of bilinear and biquadratic exchange interactions are determined. (author). 7 refs, 3 figs
Magnetic properties of Fe–Al for quenched diluted spin-1 Ising model
International Nuclear Information System (INIS)
Freitas, A.S.; Albuquerque, Douglas F. de; Fittipaldi, I.P.; Moreno, N.O.
2014-01-01
We study the phase diagram of Fe 1−q Al q alloys via the quenched site diluted spin-1 ferromagnetic Ising model by employing effective field theory. One suggests a new approach to exchange interaction between nearest neighbors of Fe that depends on the powers of the Al (q) instead of the linear dependence proposed in other papers. In such model we propose the same kind of the exchange interaction in which the iron–nickel alloys obtain an excellent theoretical description of the experimental data of the T–q phase diagram for all Al concentration q. - Highlights: • We apply the quenched Ising model spin-1 to study the properties of Fe–Al. • We employ the EFT and suggest a new approach to ferromagnetic coupling. • The new probability distribution is considered. • The phase diagram is obtained for all values of q in T–q plane
Magnetic properties of Fe–Al for quenched diluted spin-1 Ising model
Energy Technology Data Exchange (ETDEWEB)
Freitas, A.S. [Departamento de Física, Universidade Federal de Sergipe, 49100-000, São Cristovão, SE (Brazil); Coordenadoria de Física, Instituto Federal de Sergipe, 49400-000 Lagarto, SE (Brazil); Albuquerque, Douglas F. de, E-mail: douglas@ufs.br [Departamento de Física, Universidade Federal de Sergipe, 49100-000, São Cristovão, SE (Brazil); Departamento de Matemática, Universidade Federal de Sergipe, 49100-000, São Cristovão, SE (Brazil); Fittipaldi, I.P. [Representação Regional do Ministério da Ciência, Tecnologia e Inovação no Nordeste - ReNE, 50740-540 Recife, PE (Brazil); Moreno, N.O. [Departamento de Física, Universidade Federal de Sergipe, 49100-000, São Cristovão, SE (Brazil)
2014-08-01
We study the phase diagram of Fe{sub 1−q}Al{sub q} alloys via the quenched site diluted spin-1 ferromagnetic Ising model by employing effective field theory. One suggests a new approach to exchange interaction between nearest neighbors of Fe that depends on the powers of the Al (q) instead of the linear dependence proposed in other papers. In such model we propose the same kind of the exchange interaction in which the iron–nickel alloys obtain an excellent theoretical description of the experimental data of the T–q phase diagram for all Al concentration q. - Highlights: • We apply the quenched Ising model spin-1 to study the properties of Fe–Al. • We employ the EFT and suggest a new approach to ferromagnetic coupling. • The new probability distribution is considered. • The phase diagram is obtained for all values of q in T–q plane.
Two site spin correlation function in Bethe-Peierls approximation for Ising model
Energy Technology Data Exchange (ETDEWEB)
Kumar, D [Roorkee Univ. (India). Dept. of Physics
1976-07-01
Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while these results are derived by retaining that class of diagrams , which is exact on Bethe lattice.
The diluted tri-dimensional spin-one Ising model with crystal field interactions
International Nuclear Information System (INIS)
Saber, M.
1988-09-01
3D spin-one Ising models with nearest-neighbour ferromagnetic interactions with crystal-field exhibit tricritical behaviour. A new method that applies to a wide class of random systems is used to study the influence of site and bond dilution on this behaviour. We have calculated temperature-crystal-field-concentration phase diagrams and determined, in particular, the influence of dilution on the zero temperature tricritical temperature. (author). 10 refs, 8 figs
Critical properties of a ferroelectric superlattice described by a transverse spin-1/2 Ising model
International Nuclear Information System (INIS)
Tabyaoui, A; Saber, M; Baerner, K; Ainane, A
2007-01-01
The phase transition properties of a ferroelectric superlattice with two alternating layers A and B described by a transverse spin-1/2 Ising model have been investigated using the effective field theory within a probability distribution technique that accounts for the self spin correlation functions. The Curie temperature T c , polarization and susceptibility have been obtained. The effects of the transverse field and the ferroelectric and antiferroelectric interfacial coupling strength between two ferroelectric materials are discussed. They relate to the physical properties of antiferroelectric/ferroelectric superlattices
The ground-state phase diagrams of the spin-3/2 Ising model
International Nuclear Information System (INIS)
Canko, Osman; Keskin, Mustafa
2003-01-01
The ground-state spin configurations are obtained for the spin-3/2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. The calculated ground-state phase diagrams are presented on diatomic lattices, such as the square, honeycomb and sc lattices, and triangular lattice in the (Δ/z vertical bar J vertical bar ,K/ vertical bar J vertical bar) and (H/z vertical bar J vertical bar, K/ vertical bar J vertical bar) planes
International Nuclear Information System (INIS)
Battistin, C; Roudi, Y; Hertz, J; Tyrcha, J
2015-01-01
We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless–Anderson–Palmer (TAP) equations for reconstructing the connections. (paper)
Pini, Maria Gloria; Rettori, Angelo
1993-08-01
The thermodynamical properties of an alternating spin (S,s) one-dimensional (1D) Ising model with competing nearest- and next-nearest-neighbor interactions are exactly calculated using a transfer-matrix technique. In contrast to the case S=s=1/2, previously investigated by Harada, the alternation of different spins (S≠s) along the chain is found to give rise to two-peaked static structure factors, signaling the coexistence of different short-range-order configurations. The relevance of our calculations with regard to recent experimental data by Gatteschi et al. in quasi-1D molecular magnetic materials, R (hfac)3 NITEt (R=Gd, Tb, Dy, Ho, Er, . . .), is discussed; hfac is hexafluoro-acetylacetonate and NlTEt is 2-Ethyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide.
Tricritical behavior in the diluted transverse spin-1 Ising model with a longitudinal crystal field
International Nuclear Information System (INIS)
Htoutou, K.; Oubelkacem, A.; Ainane, A.; Saber, M.
2005-01-01
The transverse spin-1 Ising model with a longitudinal crystal field exhibits a tricritical behavior. Within the effective field theory with a probability distribution technique that accounts for the self-spin correlations, we have studied the influence of site dilution on this behavior and have calculated the temperature-transverse field-longitudinal crystal field-concentration phase diagrams and determined, in particular, the influence of the concentration of magnetic atoms c on the tricritical behavior. We have found that the tricritical point appears for large values of the concentration c of magnetic atoms and disappears with the increase in dilution (small values of c). Results for square lattice are calculated numerically and some interesting results are obtained. In certain ranges of values of the strength of the longitudinal crystal field D/J when it becomes sufficiently negative, we found re-entrant phenomenon, which disappears with increase in the value of the strength of the transverse field
Magnetic properties of a ferromagnet spin-S, Ising, XY and Heisenberg models semi-infinites systems
International Nuclear Information System (INIS)
Masrour, R.; Hamedoun, M.; Hourmatallah, A.; Bouslykhane, K.; Benzakour, N.
2008-01-01
The magnetic properties of a ferromagnet spin-S a disordered semi-infinite system with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Pade approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ c =(k B T c )/(2S(S+1)J b ) is studied as function of the thickness of the film and the exchange interactions in the bulk, and within the surfaces J b ,J s and J perpendicular , respectively. It is found that τ c increases with the exchange interactions of surface. The magnetic phase diagrams (τ c versus the dilution x) and the percolation threshold are obtained
Transverse spin correlations of the random transverse-field Ising model
Iglói, Ferenc; Kovács, István A.
2018-03-01
The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d =1 ,2 , and 3 dimensions. At the critical point an algebraic decay of the form ˜r-ηt is found, with a decay exponent being approximately ηt≈2 +2 d . In d =1 the results are related to dimer-dimer correlations in the random antiferromagnetic X X chain and have been tested by numerical calculations using free-fermionic techniques.
The Landau-Lifshitz equation describes the Ising spin correlation function in the free-fermion model
Rutkevich, S B
1998-01-01
We consider time and space dependence of the Ising spin correlation function in a continuous one-dimensional free-fermion model. By the Ising spin we imply the 'sign' variable, which takes alternating +-1 values in adjacent domains bounded by domain walls (fermionic world paths). The two-point correlation function is expressed in terms of the solution of the Cauchy problem for a nonlinear partial differential equation, which is proved to be equivalent to the exactly solvable Landau-Lifshitz equation. A new zero-curvature representation for this equation is presented. In turn, the initial condition for the Cauchy problem is given by the solution of a nonlinear ordinary differential equation, which has also been derived. In the Ising limit the above-mentioned partial and ordinary differential equations reduce to the sine-Gordon and Painleve III equations, respectively. (author)
Study of spin crossover nanoparticles thermal hysteresis using FORC diagrams on an Ising-like model
International Nuclear Information System (INIS)
Atitoaie, Alexandru; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2014-01-01
Recent developments in the synthesis and characterization of spin crossover (SCO) nanoparticles and their prospects of switching at molecular level turned these bistable compounds into possible candidates for replacing the materials used in recording media industry for development of solid state pressure and temperature sensors or for bringing contributions in engineering. Compared to bulk samples with the same chemical structure, SCO nanoparticles display different characteristics of the hysteretic and relaxation properties like the shift of the transition temperature towards lower values along with decrease of the hysteresis width with nanoparticles size. Using an Ising-like model with specific boundary conditions within a Monte Carlo procedure, we here reproduce most of the hysteretic properties of SCO nanoparticles by considering the interaction between spin crossover edge molecules and embedding surfactant molecules and we propose a complex analysis concerning the effect of the interactions and sizes during the thermal transition in systems of SCO nanoparticles by using the First Order Reversal Curves diagram method and by comparison with similar effects in mixed crystal systems. - Highlights: • The influence of size effects in spin crossover nanoparticles is analyzed. • The environment shifts the hysteresis loop towards lower temperatures. • First Order Reversal Curves technique is employed. • One determines the distributions of switching temperatures. • One disentangles between kinetics and non-kinetic parts of the hysteresis
Elementary excitations and the phase transition in the bimodal Ising spin glass model
International Nuclear Information System (INIS)
Jinuntuya, N; Poulter, J
2012-01-01
We show how the nature of the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference L. This 2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet. The spatial influence of the frustration must be limited and not wrap around the system if L is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating the magnetization or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass state occurs. The value p c = 0.1045(11) is in reasonable agreement with the literature
de Léséleuc, Sylvain; Weber, Sebastian; Lienhard, Vincent; Barredo, Daniel; Büchler, Hans Peter; Lahaye, Thierry; Browaeys, Antoine
2018-03-01
We study a system of atoms that are laser driven to n D3 /2 Rydberg states and assess how accurately they can be mapped onto spin-1 /2 particles for the quantum simulation of anisotropic Ising magnets. Using nonperturbative calculations of the pair potentials between two atoms in the presence of electric and magnetic fields, we emphasize the importance of a careful selection of experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1 /2 Ising models in systems with up to 49 spins, for which numerical simulations become intractable.
Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model
International Nuclear Information System (INIS)
Deviren, Bayram; Keskin, Mustafa; Canko, Osman
2009-01-01
We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, σ=±1/2 , alternated with spins that can take the four values, S=±3/2 ,±1/2 . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters
Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model
Energy Technology Data Exchange (ETDEWEB)
Deviren, Bayram [Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr; Canko, Osman [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2009-03-15
We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, {sigma}={+-}1/2 , alternated with spins that can take the four values, S={+-}3/2 ,{+-}1/2 . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.
An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model
Energy Technology Data Exchange (ETDEWEB)
Roberto Viana, J.; Salmon, Octávio R. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); Ricardo de Sousa, J. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); National Institute of Science and Technology for Complex Systems, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus, AM (Brazil); Neto, Minos A.; Padilha, Igor T. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil)
2014-11-15
We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value k{sub B}T{sub c}/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained. - Highlights: • We developed spin models to study real magnetic systems. • We study the thermodynamic and magnetic properties of the ferromagnetism. • We enhanced a mean-field theory applied in spins models.
Entanglement of two blocks of spins in the critical Ising model
Facchi, P.; Florio, G.; Invernizzi, C.; Pascazio, S.
2008-11-01
We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and 2. In the general case, the critical entropy is shown to be additive when d→∞ . Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d . This formula is in excellent agreement with numerical results.
International Nuclear Information System (INIS)
Atitoaie, Alexandru; Tanasa, Radu; Enachescu, Cristian
2012-01-01
Spin crossover compounds are photo-magnetic bistable molecular magnets with two states in thermodynamic competition: the diamagnetic low-spin state and paramagnetic high-spin state. The thermal transition between the two states is often accompanied by a wide hysteresis, premise for possible application of these materials as recording media. In this paper we study the influence of the system's size on the thermal hysteresis loops using Monte Carlo simulations based on an Arrhenius dynamics applied for an Ising like model with long- and short-range interactions. We show that using appropriate boundary conditions it is possible to reproduce both the drop of hysteresis width with decreasing particle size, the hysteresis shift towards lower temperatures and the incomplete transition, as in the available experimental data. The case of larger systems composed by several sublattices is equally treated reproducing the shrinkage of the hysteresis loop's width experimentally observed. - Highlights: ► A study concerning size effects in spin crossover nanoparticles hysteresis is presented. ► An Ising like model with short- and long-range interactions and Arrhenius dynamics is employed. ► In open boundary system the hysteresis width decreases with particle size. ► With appropriate environment, hysteresis loop is shifted towards lower temperature and transition is incomplete.
An Ising spin state explanation for financial asset allocation
Horvath, Philip A.; Roos, Kelly R.; Sinha, Amit
2016-03-01
We build on the developments in the application of statistical mechanics, notably the identity of the spin degree of freedom in the Ising model, to explain asset price dynamics in financial markets with a representative agent. Specifically, we consider the value of an individual spin to represent the proportional holdings in various assets. We use partial moment arguments to identify asymmetric reactions to information and develop an extension of a plunging and dumping model. This unique identification of the spin is a relaxation of the conventional discrete state limitation on an Ising spin to accommodate a new archetype in Ising model-finance applications wherein spin states may take on continuous values, and may evolve in time continuously, or discretely, depending on the values of the partial moments.
Chen, Jiahui; Zhou, Hui; Duan, Changkui; Peng, Xinhua
2017-03-01
Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and W states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and W states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the W state, we find a standard way to prepare the W state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.
International Nuclear Information System (INIS)
Zimmer, F.M.; Magalhaes, S.G.
2007-01-01
The one-step replica symmetry breaking is used to study the competition between spin glass (SG) and antiferromagnetic order (AF) in two-sublattice fermionic Ising SG models in the presence of a transverse Γ and a parallel H magnetic fields. Inter- and intra-sublattice exchange interactions following Gaussian distributions are considered. The problem is formulated in a Grassmann path integral formalism within the static ansatz. Results show that H favors the non-ergodic mixed phase (AF+SG) and it destroys the AF. The Γ suppresses the magnetic orders, and the intra-sublattice interaction can introduce a discontinuous phase transition
Wetting and layering transitions of a spin-1/2 Ising model in a random transverse field
International Nuclear Information System (INIS)
Bahmad, L.; Benyoussef, A.; El-Kenz, A.; Ez-Zahraouy, H.
2000-09-01
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability p, above which wetting and layering transitions disappear. (author)
Fermions as generalized Ising models
Directory of Open Access Journals (Sweden)
C. Wetterich
2017-04-01
Full Text Available We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.
Energy Technology Data Exchange (ETDEWEB)
Ertaş, Mehmet, E-mail: mehmetertas@erciyes.edu.tr; Keskin, Mustafa
2015-08-15
Herein we study the dynamic phase transition properties for the mixed spin-(1/2, 1) Ising model on a square lattice under a time-dependent magnetic field by means of the effective-field theory (EFT) with correlations based on Glauber dynamics. We present the dynamic phase diagrams in the reduced magnetic field amplitude and reduced temperature plane and find that the phase diagrams exhibit dynamic tricitical behavior, multicritical and zero-temperature critical points as well as reentrant behavior. We also investigate the influence of frequency (ω) and observe that for small values of ω the mixed phase disappears, but for high values it appears and the system displays reentrant behavior as well as a critical end point. - Highlights: • Dynamic behaviors of a ferrimagnetic mixed spin (1/2, 1) Ising system are studied. • We examined the effects of the Hamiltonian parameters on the dynamic behaviors. • The phase diagrams are obtained in (T-h) plane. • The dynamic phase diagrams exhibit the dynamic tricritical and reentrant behaviors.
International Nuclear Information System (INIS)
Ertaş, Mehmet; Keskin, Mustafa
2015-01-01
Herein we study the dynamic phase transition properties for the mixed spin-(1/2, 1) Ising model on a square lattice under a time-dependent magnetic field by means of the effective-field theory (EFT) with correlations based on Glauber dynamics. We present the dynamic phase diagrams in the reduced magnetic field amplitude and reduced temperature plane and find that the phase diagrams exhibit dynamic tricitical behavior, multicritical and zero-temperature critical points as well as reentrant behavior. We also investigate the influence of frequency (ω) and observe that for small values of ω the mixed phase disappears, but for high values it appears and the system displays reentrant behavior as well as a critical end point. - Highlights: • Dynamic behaviors of a ferrimagnetic mixed spin (1/2, 1) Ising system are studied. • We examined the effects of the Hamiltonian parameters on the dynamic behaviors. • The phase diagrams are obtained in (T-h) plane. • The dynamic phase diagrams exhibit the dynamic tricritical and reentrant behaviors
Ising models and soliton equations
International Nuclear Information System (INIS)
Perk, J.H.H.; Au-Yang, H.
1985-01-01
Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained
Hyperscaling breakdown and Ising spin glasses: The Binder cumulant
Lundow, P. H.; Campbell, I. A.
2018-02-01
Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.
The spin-3/2 Ising model AFM/AFM two-layer lattice with crystal field
International Nuclear Information System (INIS)
Yigit, A.; Albayrak, E.
2010-01-01
The spin-3/2 Ising model is investigated for the case of antiferromagnetic (AFM/AFM) interactions on the two-layer Bethe lattice by using the exact recursion relations in a pairwise approach for given coordination numbers q=3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state (GS) phase diagrams are obtained on the different planes in detail and then the temperature dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q, therefore, tricritical points. It was also found that the system exhibits double-critical end points and isolated points. The model also presents two Neel temperatures, TN, and the existence of which leads to the reentrant behavior.
International Nuclear Information System (INIS)
Gudyma, Iu.; Maksymov, A.; Spinu, L.
2015-01-01
Highlights: • We study the thermal hysteresis in spin-crossover nanoparticles with stochastic perturbation. • The dependence of system behavior on its dimensionality and size were examined. • The spin-crossover compounds where described by breathing crystal field Ising-like model. • The fluctuations may enlarge the hysteresis width which is dependent on the system size. - Abstract: The spin-crossover nanoparticles of different sizes and stochastic perturbations in external field taking into account the influence of the dimensionality of the lattice was studied. The analytical tools used for the investigation of spin-crossover system are based on an Ising-like model described using of the breathing crystal field concept. The changes of transition temperatures characterizing the systems’ bistable properties for 2D and 3D lattices, and their dependence on its size and fluctuations strength were obtained. The state diagrams with hysteretic and non-hysteretic behavior regions have also been determined.
Energy Technology Data Exchange (ETDEWEB)
Gudyma, Iu. [Department of General Physics, Chernivtsi National University, Chernivtsi 58012 (Ukraine); Maksymov, A., E-mail: maxyartur@gmail.com [Department of General Physics, Chernivtsi National University, Chernivtsi 58012 (Ukraine); Advanced Material Research Institute (AMRI), University of New Orleans, New Orleans, LA 70148 (United States); Spinu, L. [Advanced Material Research Institute (AMRI), University of New Orleans, New Orleans, LA 70148 (United States); Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)
2015-10-15
Highlights: • We study the thermal hysteresis in spin-crossover nanoparticles with stochastic perturbation. • The dependence of system behavior on its dimensionality and size were examined. • The spin-crossover compounds where described by breathing crystal field Ising-like model. • The fluctuations may enlarge the hysteresis width which is dependent on the system size. - Abstract: The spin-crossover nanoparticles of different sizes and stochastic perturbations in external field taking into account the influence of the dimensionality of the lattice was studied. The analytical tools used for the investigation of spin-crossover system are based on an Ising-like model described using of the breathing crystal field concept. The changes of transition temperatures characterizing the systems’ bistable properties for 2D and 3D lattices, and their dependence on its size and fluctuations strength were obtained. The state diagrams with hysteretic and non-hysteretic behavior regions have also been determined.
Statistical mechanics of the cluster Ising model
International Nuclear Information System (INIS)
Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko
2011-01-01
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Statistical mechanics of the cluster Ising model
Energy Technology Data Exchange (ETDEWEB)
Smacchia, Pietro [SISSA - via Bonomea 265, I-34136, Trieste (Italy); Amico, Luigi [CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia Universita di Catania, C/O ed. 10, viale Andrea Doria 6, I-95125 Catania (Italy); Facchi, Paolo [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Fazio, Rosario [NEST, Scuola Normale Superiore and Istituto Nanoscienze - CNR, 56126 Pisa (Italy); Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Florio, Giuseppe; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Vedral, Vlatko [Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom)
2011-08-15
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Highly optimized simulations on single- and multi-GPU systems of the 3D Ising spin glass model
Lulli, M.; Bernaschi, M.; Parisi, G.
2015-11-01
We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: (i) the implementation of efficient memory access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); (ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and (iii) a multi-GPU version based on a combination of MPI and CUDA streams. Cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes.
Ising model for packet routing control
International Nuclear Information System (INIS)
Horiguchi, Tsuyoshi; Takahashi, Hideyuki; Hayashi, Keisuke; Yamaguchi, Chiaki
2004-01-01
For packet routing control in computer networks, we propose an Ising model which is defined in order to express competition among a queue length and a distance from a node with a packet to its destination node. By introducing a dynamics for a mean-field value of an Ising spin, we show by computer simulations that effective control of packet routing through priority links is possible
Ladder Ising spin configurations. Pt. 1. Heat capacity
International Nuclear Information System (INIS)
Mejdani, R.; Lambros, A.
1996-01-01
We consider a ladder Ising spin model (with two coupled Ising spin chains), characterized by two couplings (interchain and intrachain couplings), to study in detail, in an analytical way, its thermal behaviour and particularly the variation of the specific heat versus temperature, the ratio of interaction constants, and the magnetic field. It is interesting that when the competition between interchain and intrachain interactions is strong the specific heat exhibits a double peak and when the competition is not so strong the specific heat has a single peak. Further, without entering into details, we give, in a numerical way, some similar results for more complicated ladder configurations (with more than two linear Ising chains). The spin-1/2 ladders or systems of spin chains may be realized in nature by vanadyl pyrophosphate ((VO) 2 P 2 O 7 ) or similar materials. All these intermediate systems are today important to gain further insight into the physics of one-dimensional spin chains and two-dimensional high-T c spin systems, both of which have shown interesting and unusual magnetic and superconducting properties. It is plausible that experimental and theoretical studies of ladders may lead to other interesting physical phenomena. (orig.)
Punya Jaroenjittichai, Atchara; Laosiritaworn, Yongyut
2017-09-01
In this work, the stock-price versus economic-field hysteresis was investigated. The Ising spin Hamiltonian was utilized as the level of ‘disagreement’ in describing investors’ behaviour. The Ising spin directions were referred to an investor’s intention to perform his action on trading his stock. The periodic economic variation was also considered via the external economic-field in the Ising model. The stochastic Monte Carlo simulation was performed on Ising spins, where the steady-state excess demand and supply as well as the stock-price were extracted via the magnetization. From the results, the economic-field parameters and market temperature were found to have significant effect on the dynamic magnetization and stock-price behaviour. Specifically, the hysteresis changes from asymmetric to symmetric loops with increasing market temperature and economic-field strength. However, the hysteresis changes from symmetric to asymmetric loops with increasing the economic-field frequency, when either temperature or economic-field strength is large enough, and returns to symmetric shape at very high frequencies. This suggests competitive effects among field and temperature factors on the hysteresis characteristic, implying multi-dimensional complicated non-trivial relationship among inputs-outputs. As is seen, the results reported (over extensive range) can be used as basis/guideline for further analysis/quantifying how economic-field and market-temperature affect the stock-price distribution on the course of economic cycle.
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
Hennecke, M.
1997-01-01
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
International Nuclear Information System (INIS)
Augusiak, R; Cucchietti, F M; Lewenstein, M; Haake, F
2010-01-01
In this paper, we introduce a quantum generalization of classical kinetic Ising models (KIM), described by a certain class of quantum many-body master equations. Similarly to KIMs with detailed balance that are equivalent to certain Hamiltonian systems, our models reduce to a set of Hamiltonian systems determining the dynamics of the elements of the many-body density matrix. The ground states of these Hamiltonians are well described by the matrix product, or pair entangled projected states. We discuss critical properties of such Hamiltonians, as well as entanglement properties of their low-energy states.
International Nuclear Information System (INIS)
Castro-Alvaredo, Olalla A; Fring, Andreas
2009-01-01
We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry, we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turn out to be unique with the sole assumption that the Dyson map is Hermitian. Finally, we analyse the magnetization of the chain in the z- and x-direction.
Phase transitions of a spin-one Ising ferromagnetic superlattice
International Nuclear Information System (INIS)
Saber, A.
2001-09-01
Using the effective field theory with a probability distribution technique, the magnetic properties in an infinite superlattice consisting of two different ferromagnets are studied in a spin-one Ising model. The dependence of the Curie temperatures are calculated as a function of two slabs in one period and as a function of the intra- and interlayer exchange interactions. A critical value of the exchange reduced interaction above which the interface magnetism appears is found. (author)
Energy Technology Data Exchange (ETDEWEB)
Oh, Suhk Kun [Chungbuk National University, Chungbuk (Korea, Republic of)
2006-01-15
As an extension of our previous work on the relationship between time in Monte Carlo simulation and time in the continuous master equation in the infinit-range Glauber kinetic Ising model in the absence of any magnetic field, we explored the same model in the presence of a static magnetic field. Monte Carlo steps per spin as time in the MC simulations again turns out to be proportional to time in the master equation for the model in relatively larger static magnetic fields at any temperature. At and near the critical point in a relatively smaller magnetic field, the model exhibits a significant finite-size dependence, and the solution to the Suzuki-Kubo differential equation stemming from the master equation needs to be re-scaled to fit the Monte Carlo steps per spin for the system with different numbers of spins.
Magnetic properties and thermodynamics of decorated Ising chain with pendants of arbitrary spin
Energy Technology Data Exchange (ETDEWEB)
Li Wei, E-mail: liwei-b09@mails.gucas.ac.c [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049 (China); Department of Physics, Beihang University, Beijing 100191 (China); Gong Shoushu [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049 (China); Chen Ziyu [Department of Physics, Beihang University, Beijing 100191 (China); Zhao Yang [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049 (China); Su Gang, E-mail: gsu@gucas.ac.c [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049 (China)
2010-05-31
The decorated Ising chain with pendants of arbitrary spin and the single-ion anisotropy is exactly solved by the transfer matrix method. The solutions reveal abundant novel properties than the conventional one-dimensional Ising model. It is compared with the experimental data of a necklace-like molecule-based magnet, that gives a qualitative consistency.
Magnetic properties and thermodynamics of decorated Ising chain with pendants of arbitrary spin
International Nuclear Information System (INIS)
Li Wei; Gong Shoushu; Chen Ziyu; Zhao Yang; Su Gang
2010-01-01
The decorated Ising chain with pendants of arbitrary spin and the single-ion anisotropy is exactly solved by the transfer matrix method. The solutions reveal abundant novel properties than the conventional one-dimensional Ising model. It is compared with the experimental data of a necklace-like molecule-based magnet, that gives a qualitative consistency.
International Nuclear Information System (INIS)
Atitoaie, Alexandru; Stoleriu, Laurentiu; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2016-01-01
The scientific community is manifesting a high research interest on spin crossover compounds and their recently synthesized nanoparticles, due to their various appealing properties, such as the bistability between a diamagnetic low spin state and a paramagnetic high spin state (HS), inter-switchable by temperature or pressure changes, light irradiation or magnetic field. The utility of these compounds showing hysteresis covers a broad area of applications, from the development of more efficient designs of temperature and pressure sensors to automotive and aeronautic industries and even a new type of molecular actuators. We are proposing in this work a study regarding the kinetic effects and the distribution of reversible and irreversible components on the thermal hysteresis of spin crossover nanoparticulated systems. We are considering here tridimensional systems with different sizes and also systems of nanoparticles with a Gaussian size distribution. The correlations between the kinetics of the thermal hysteresis, the distributions of sizes and intermolecular interactions and the transition temperature distributions were established by using the FORC (First Order Reversal Curves) method using a Monte Carlo technique within an Ising-like system.
Energy Technology Data Exchange (ETDEWEB)
Atitoaie, Alexandru, E-mail: atitoaie@phys-iasi.ro [Department. of Physics, “Alexandru Ioan Cuza” University, 700506 Iasi (Romania); National Institute of Research and Development for Technical Physics, Iasi (Romania); Stoleriu, Laurentiu [Department. of Physics, “Alexandru Ioan Cuza” University, 700506 Iasi (Romania); Tanasa, Radu [Department. of Physics, “Alexandru Ioan Cuza” University, 700506 Iasi (Romania); Department of Engineering, University of Cambridge, CB2 1PZ Cambridge (United Kingdom); Stancu, Alexandru; Enachescu, Cristian [Department. of Physics, “Alexandru Ioan Cuza” University, 700506 Iasi (Romania)
2016-04-01
The scientific community is manifesting a high research interest on spin crossover compounds and their recently synthesized nanoparticles, due to their various appealing properties, such as the bistability between a diamagnetic low spin state and a paramagnetic high spin state (HS), inter-switchable by temperature or pressure changes, light irradiation or magnetic field. The utility of these compounds showing hysteresis covers a broad area of applications, from the development of more efficient designs of temperature and pressure sensors to automotive and aeronautic industries and even a new type of molecular actuators. We are proposing in this work a study regarding the kinetic effects and the distribution of reversible and irreversible components on the thermal hysteresis of spin crossover nanoparticulated systems. We are considering here tridimensional systems with different sizes and also systems of nanoparticles with a Gaussian size distribution. The correlations between the kinetics of the thermal hysteresis, the distributions of sizes and intermolecular interactions and the transition temperature distributions were established by using the FORC (First Order Reversal Curves) method using a Monte Carlo technique within an Ising-like system.
Gálisová, Lucia; Strečka, Jozef
2018-05-01
The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | - ΔSisomin | ∝hn, where n depends basically on the ground-state spin ordering.
An Ising model for metal-organic frameworks
Höft, Nicolas; Horbach, Jürgen; Martín-Mayor, Victor; Seoane, Beatriz
2017-08-01
We present a three-dimensional Ising model where lines of equal spins are frozen such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH4) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.
The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation
International Nuclear Information System (INIS)
Canko, O.; Albayrak, E.; Keskin, M.
2005-01-01
In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number
Dynamical TAP equations for non-equilibrium Ising spin glasses
DEFF Research Database (Denmark)
Roudi, Yasser; Hertz, John
2011-01-01
We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....
International Nuclear Information System (INIS)
Monthus, Cécile
2015-01-01
For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco (1979 Phys. Rev. D 19 3173) is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent ν = 1. Recently, Miyazaki and Nishimori (2013 Phys. Rev. E 87 032154) have proposed to study the disordered quantum Ising model in dimensions d > 1 by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the inequivalence of directions of their approach, we propose here an alternative procedure where the d directions are treated on the same footing. For the pure model, this leads to the correlation length exponents ν ≃ 0.625 in d = 2 (to be compared with the 3D classical Ising model exponent ν ≃ 0.63) and ν ≃ 0.5018 (to be compared with the 4D classical Ising model mean-field exponent ν = 1/2). For the disordered model in dimension d = 2, either ferromagnetic or spin-glass, the numerical application of the renormalization rules to samples of linear size L = 4096 yields that the transition is governed by an Infinite Disorder Fixed Point, with the activated exponent ψ ≃ 0.65, the typical correlation exponent ν typ ≃ 0.44 and the finite-size correlation exponent ν FS ≃ 1.25. We discuss the similarities and differences with the Strong Disorder Renormalization results. (paper)
Ertaş, Mehmet
2015-09-01
Keskin and Ertaş (2009) presented a study of the magnetic properties of a mixed spin (2, 5/2) ferrimagnetic Ising model within an oscillating magnetic field. They employed dynamic mean-field calculations to find the dynamic phase transition temperatures, the dynamic compensation points of the model and to present the dynamic phase diagrams. In this work, we extend the study and investigate the dynamic hysteresis behaviors for the two-dimensional (2D) mixed spin (2, 5/2) ferrimagnetic Ising model on a hexagonal lattice in an oscillating magnetic field within the framework of dynamic mean-field calculations. The dynamic hysteresis curves are obtained for both the ferromagnetic and antiferromagnetic interactions and the effects of the Hamiltonian parameters on the dynamic hysteresis behaviors are discussed in detail. The thermal behaviors of the coercivity and remanent magnetizations are also investigated. The results are compared with some theoretical and experimental works and a qualitatively good agreement is found. Finally, the dynamic phase diagrams depending on the frequency of an oscillating magnetic field in the plane of the reduced temperature versus magnetic field amplitude is examined and it is found that the dynamic phase diagrams display richer dynamic critical behavior for higher values of frequency than for lower values.
Mixed spin-5/2 and spin-2 Ising ferrimagnetic system on the Bethe lattice
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, PB 63 46000, Safi (Morocco); Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2015-11-01
The magnetic properties of spins-S and σ Ising model on the Bethe lattice have been investigated by using the Monte Carlo simulation. The thermal total magnetization and magnetization of spins S and σ with the different exchange interactions, different external magnetic field and different temperatures have been studied. The critical temperature and compensation temperature have been deduced. The magnetic hysteresis cycle of Ising ferrimagnetic system on the Bethe lattice has been deduced for different values of exchange interactions between the spins S and σ, for different values of crystal field and for different sizes. The magnetic coercive filed has been deduced. - Highlights: • The magnetic properties of Bethe lattice have been investigated. • The critical temperature and compensation temperature have been deduced. • The magnetic coercive filed has been deduced.
Diagonalization of replicated transfer matrices for disordered Ising spin systems
International Nuclear Information System (INIS)
Nikoletopoulos, T; Coolen, A C C
2004-01-01
We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbour bonds and/or random fields, possibly in combination with (random) long range bonds. Our method is based on transforming the original eigenvalue problem for a 2 n x 2 n matrix (where n → 0) into an eigenvalue problem for integral operators. We first develop our formalism for the Ising chain with random bonds and fields, where we recover known results. We then apply our methods to models of spins which interact simultaneously via a one-dimensional ring and via more complex long-range connectivity structures, e.g., (1 + ∞)-dimensional neural networks and 'small-world' magnets. Numerical simulations confirm our predictions satisfactorily
An extended chain Ising model and its Glauber dynamics
International Nuclear Information System (INIS)
Zhao Xing-Yu; Fan Xiao-Hui; Huang Yi-Neng; Huang Xin-Ru
2012-01-01
It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model, single spin double-well potentials and a pure phonon heat bath of a specific energy exchange with the spins. The extension method is easy to apply to high dimensional cases. Then the single spin-flip probability (rate) of the ECI model is deduced based on the Boltzmann principle and general statistical principles of independent events and the model is simplified to an extended chain Glauber—Ising (ECGI) model. Moreover, the relaxation dynamics of the ECGI model were simulated by the Monte Carlo method and a comparison with the predictions of the special chain Glauber—Ising (SCGI) model was presented. It was found that the results of the two models are consistent with each other when the Ising chain length is large enough and temperature is relative low, which is the most valuable case of the model applications. These show that the ECI model will provide a firm physical base for the widely used single spin-flip rate proposed by Glauber and a possible route to obtain the single spin-flip rate of other form and even the multi-spin-flip rate. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Phase diagrams of a spin-1/2 transverse Ising model with three-peak random field distribution
International Nuclear Information System (INIS)
Bassir, A.; Bassir, C.E.; Benyoussef, A.; Ez-Zahraouy, H.
1996-07-01
The effect of the transverse magnetic field on the phase diagrams structures of the Ising model in a random longitudinal magnetic field with a trimodal symmetric distribution is investigated within a finite cluster approximation. We find that a small magnetizations ordered phase (small ordered phase) disappears completely for a sufficiently large value of the transverse field or/and large value of the concentration of the disorder of the magnetic field. Multicritical behaviour and reentrant phenomena are discussed. The regions where the tricritical, reentrant phenomena and the small ordered phase persist are delimited as a function of the transverse field and the concentration p. Longitudinal magnetizations are also presented. (author). 33 refs, 6 figs
Energy Technology Data Exchange (ETDEWEB)
Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, PB 63 46000 Safi (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2016-01-01
The magnetic properties of alternate mixed spin-5/2 and spin-2 Ising model on the Bethe lattice have been studied by using the Monte Carlo simulations. The ground state phase diagrams of alternate mixed spin-5/2 and spin-2 Ising model on the Bethe lattice has been obtained. The thermal total magnetization and magnetization of spins-5/2 and spin-2 with the different exchange interactions, external magnetic field and temperatures have been studied. The critical temperature have been deduced. The magnetic hysteresis cycle on the Bethe lattice has been deduced for different values of exchange interactions, for different values of crystal field and for different sizes. The magnetic coercive field has been deduced. - Highlights: • The alternate mixed spin-5/2 and -2 on the Bethe lattice is studied. • The critical temperature has been deduced. • The magnetic coercive filed has been deduced.
One-dimensional Ising model with multispin interactions
Turban, Loïc
2016-09-01
We study the spin-1/2 Ising chain with multispin interactions K involving the product of m successive spins, for general values of m. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions and we calculate the two-spin correlation function. When placed in an external field H the system is shown to be self-dual. Using another change of spin variables the one-dimensional Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions K and H. The 2D system, with size m × N/m, has the topology of a cylinder with helical BC. In the thermodynamic limit N/m\\to ∞ , m\\to ∞ , a 2D critical singularity develops on the self-duality line, \\sinh 2K\\sinh 2H=1.
Mixed spin-3/2 and spin-5/2 Ising system on the Bethe lattice
International Nuclear Information System (INIS)
Albayrak, Erhan; Yigit, Ali
2006-01-01
In order to study the critical behaviors of the half-integer mixed spin-3/2 and spin-5/2 Blume-Capel Ising ferrimagnetic system, we have used the exact recursion relations on the Bethe lattice. The system was studied for the coordination numbers with q=3, 4, 5 and 6, and the obtained phase diagrams are illustrated on the (kT c /|J|,D A /|J|) plane for constant values of D B /|J|, the reduced crystal field of the sublattice with spin-5/2, and on the (kT c /|J|,D B /|J|) plane for constant values of D A /|J|, the reduced crystal field of the sublattice with spin-3/2, for q=3 only, since the cases corresponding to q=4, 5 and 6 reproduce results similar to the case for q=3. In addition we have also presented the phase diagram with equal strengths of the crystal fields for q=3, 4, 5 and 6. Besides the second- and first-order phase transitions, the system also exhibits compensation temperatures for appropriate values of the crystal fields. In this mixed spin system while the second-order phase transition lines never cut the reduced crystal field axes as in the single spin type spin-3/2 and spin-5/2 Ising models separately, the first-order phase transition lines never connect to the second-order phase transition lines and they end at the critical points, therefore the system does not give any tricritical points. In addition to this, this mixed-spin model exhibits one or two compensation temperatures depending on the values of the crystal fields, as a result the compensation temperature lines show reentrant behavior
Microscopic energy flows in disordered Ising spin systems
International Nuclear Information System (INIS)
Agliari, E; Casartelli, M; Vezzani, A
2010-01-01
An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder, i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier discretized picture. Then, we work out a linearized 'mean-field approximation', where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on generic discrete structures
International Nuclear Information System (INIS)
Temizer, Umuet; Keskin, Mustafa; Canko, Osman
2009-01-01
The dynamic behavior of a two-sublattice spin-1 Ising model with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=1 and S=1. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transition rates to construct the mean-field dynamical equations. Firstly, we study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the average magnetizations in a period, which is also called the dynamic magnetizations, to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the total dynamic magnetization as a function of the temperature is investigated to find the types of the compensation behavior. Dynamic phase diagrams are calculated for both DPT points and dynamic compensation effect. Phase diagrams contain the paramagnetic (p) and antiferromagnetic (af) phases, the p+af and nm+p mixed phases, nm is the non-magnetic phase, and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters. For D 0 >3.8275, H 0 is the magnetic field amplitude, the compensation effect does not appear in the system.
Energy Technology Data Exchange (ETDEWEB)
Temizer, Umuet [Department of Physics, Bozok University, 66100 Yozgat (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr; Canko, Osman [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2009-10-15
The dynamic behavior of a two-sublattice spin-1 Ising model with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins {sigma}=1 and S=1. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transition rates to construct the mean-field dynamical equations. Firstly, we study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the average magnetizations in a period, which is also called the dynamic magnetizations, to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the total dynamic magnetization as a function of the temperature is investigated to find the types of the compensation behavior. Dynamic phase diagrams are calculated for both DPT points and dynamic compensation effect. Phase diagrams contain the paramagnetic (p) and antiferromagnetic (af) phases, the p+af and nm+p mixed phases, nm is the non-magnetic phase, and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters. For D<2.835 and H{sub 0}>3.8275, H{sub 0} is the magnetic field amplitude, the compensation effect does not appear in the system.
Thue-Morse quantum Ising model
International Nuclear Information System (INIS)
Doria, M.M.; Nori, F.; Satija, I.I.
1989-01-01
We study the one-dimensional quantum Ising model in a transverse magnetic field where the exchange couplings are ordered according to the Thue-Morse (TM) sequence. At zero temperature, this model is equivalent to a two-dimensional classical Ising model in a magnetic field with TM aperiodicity along one direction. We compute the order parameter (magnetization) of the chain and the scaling behavior of the energy spectrum when the system undergoes a phase transition. Analogous to the quasiperiodic (QP) quantum Ising chain, the onset of long-range order is signaled by a nonanaliticity in the exponent δ which describes the scaling of the total bandwidth with the size of the chain. The critical spin-coupling can be computed analytically and it is found to be lower than the QP case. Furthermore, the energy bands are found to be narrower than the corresponding QP chain. The former and latter results are consistent with the fact that the present structure has a degree of ordering intermediate between QP and random
Quantum simulation of transverse Ising models with Rydberg atoms
Schauss, Peter
2018-04-01
Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.
Effective field renormalization group approach for Ising lattice spin systems
Fittipaldi, Ivon P.
1994-03-01
A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.
Simulations of ground state fluctuations in mean-field Ising spin glasses
International Nuclear Information System (INIS)
Boettcher, Stefan
2010-01-01
The scaling of fluctuations in the distribution of ground state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the extremal optimization heuristic across a range of different models on sparse and dense graphs. These models exhibit very diverse behaviors, and an asymptotic extrapolation is often complicated by higher-order corrections in size. The clearest picture, in fact, emerges from the study of graph bipartitioning, a combinatorial optimization problem closely related to spin glasses. Asides from two-spin interactions with discrete bonds, we also consider problems with Gaussian bonds and three-spin interactions, which behave quite differently
Arian Zad, Hamid; Ananikian, Nerses
2017-11-01
We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.
International Nuclear Information System (INIS)
Wei Guozhu; Miao Hailing
2009-01-01
The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
The Ising model coupled to 2d orders
Glaser, Lisa
2018-04-01
In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase diagram in terms of the Wick rotation parameter β and the Ising coupling j and find that the matter and the causal sets together give rise to an interesting phase structure. The couplings give rise to five different phases. The causal sets take on random or crystalline characteristics as described in Surya (2012 Class. Quantum Grav. 29 132001) and the Ising model can be correlated or uncorrelated on the random orders and correlated, uncorrelated or anti-correlated on the crystalline orders. We find that at least one new phase transition arises, in which the Ising spins push the causal set into the crystalline phase.
Correlation effects in the Ising model in an external field
International Nuclear Information System (INIS)
Borges, H.E.; Silva, P.R.
1983-01-01
The thermodynamic properties of the spin-1/2 Ising Model in an external field are evaluated through the use of the exponential differential operator method and Callen's exact relations. The correlations effects are treated in a phenomenological approach and the results are compared with other treatments. (Author) [pt
Susceptibility and magnetization of a random Ising model
Energy Technology Data Exchange (ETDEWEB)
Kumar, D; Srivastava, V [Roorkee Univ. (India). Dept. of Physics
1977-08-01
The susceptibility of a bond disordered Ising model is calculated by configurationally averaging an Ornstein-Zernike type of equation for the two spin correlation function. The equation for the correlation function is derived using a diagrammatic method due to Englert. The averaging is performed using bond CPA. The magnetization is also calculated by averaging in a similar manner a linearised molecular field equation.
DEFF Research Database (Denmark)
Roudi, Yasser; Tyrcha, Joanna; Hertz, John
2009-01-01
(dansk abstrakt findes ikke) We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we...... extract the optimal couplings for subsets of size up to $200$ neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods -- inversion...... of the Thouless-Anderson-Palmer equations and an approximation proposed by Sessak and Monasson -- are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate...
Universal amplitude ratios in the 3D Ising model
International Nuclear Information System (INIS)
Caselle, M.; Hasenbusch, M.
1998-01-01
We present a high precision Monte Carlo study of various universal amplitude ratios of the three dimensional Ising spin model. Using state of the art simulation techniques we studied the model close to criticality in both phases. Great care was taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain C + /C - =4.75(3), f +,2nd /f -,2nd =1.95(2) and u * =14.3(1). Our results are compatible with those obtained by field theoretic methods applied to the φ 4 theory and high and low temperature series expansions of the Ising model. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Batı, Mehmet, E-mail: mehmet.bati@erdogan.edu.tr [Department of Physics, Recep Tayyip Erdoğan University, 53100 Rize (Turkey); Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2017-05-15
The hysteresis properties of a kinetic mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice are studied by means of the dynamic mean field theory. In the present study, the effects of the nearest-neighbor interaction, temperature, frequency of oscillating magnetic field and the exchange anisotropy on the hysteresis properties of the kinetic system are discussed in detail. A number of interesting phenomena such as the shape of hysteresis loops with one, two, three and inverted-hysteresis/proteresis (butterfly shape hysteresis) have been obtained. Finally, the obtained results are compared with some experimental and theoretical results and a qualitatively good agreement is found.
Acharyya, Muktish
2017-07-01
The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.
Multiple Time Series Ising Model for Financial Market Simulations
International Nuclear Information System (INIS)
Takaishi, Tetsuya
2015-01-01
In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated
Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
Sastre, Francisco; Dornic, Ivan; Chaté, Hugues
2003-01-01
We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points, the large-time ``fluctuation-dissipation ratio'' $X_\\infty$ is a universal amplitude ratio and find in particular $X_\\infty \\approx 0.33(2)$ and $X_\\infty = 1/2$ for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.
Effective field treatment of the annealed bond-dilute transverse Ising model
International Nuclear Information System (INIS)
Silva, P.R.; Sa Barreto, F.C. de
1983-01-01
The dilution of the spin-1/2 transverse Ising Model is studied by means of an effective field type treatment based on an extension of Callen's relation to the present model. The thermodynamics of the diluted model is obtained and the results are shown to be an improvement over the standard mean field treatment. The results are also compared with the Monte Carlo calculation for the spin-infinite transverse Ising Model. (Author) [pt
Noise as a Probe of Ising Spin Glass Transitions
Chen, Zhi; Yu, Clare
2009-03-01
Noise is ubiquitous and and is often viewed as a nuisance. However, we propose that noise can be used as a probe of the fluctuations of microscopic entities, especially in the vicinity of a phase transition. In recent work we have used simulations to show that the noise increases in the vicinity of phase transitions of ordered systems. We have recently turned our attention to noise near the phase transitions of disordered systems. In particular, we are studying the noise near Ising spin glass transitions using Monte Carlo simulations. We monitor the system as a function of temperature. At each temperature, we obtain the time series of quantities characterizing the properties of the system, i.e., the energy and magnetization. We look at different quantities, such as the noise power spectrum and the second spectrum of the noise, to analyze the fluctuations.
International Nuclear Information System (INIS)
Kawamoto, Tohru; Abe, Shuji
2005-01-01
We investigated the switching behavior of small particles of an Ising-like model under constant excitation by means of Monte Carlo simulations to study photoinduced spinstate switching in nanoparticles of transition metal complexes. The threshold intensity required for that switching becomes drastically small in small particles with diameter of less than 10 pseudospins. This lower intensity results enhancement of the pseudospin fluctuation at the surface in the small particles. Our result might originate the increase of the photoinduced magnetization in nanoparticles of a Mo-Cu cyanide
Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.
Wu, Jianda; Kormos, Márton; Si, Qimiao
2014-12-12
A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.
Hexagonal type Ising nanowire with mixed spins: Some dynamic behaviors
International Nuclear Information System (INIS)
Kantar, Ersin; Kocakaplan, Yusuf
2015-01-01
The dynamic behaviors of a mixed spin (1/2–1) hexagonal Ising nanowire (HIN) with core–shell structure in the presence of a time dependent magnetic field are investigated by using the effective-field theory with correlations based on the Glauber-type stochastic dynamics (DEFT). According to the values of interaction parameters, temperature dependence of the dynamic magnetizations, the hysteresis loop areas and the dynamic correlations are investigated to characterize the nature (first- or second-order) of the dynamic phase transitions (DPTs). Dynamic phase diagrams, including compensation points, are also obtained. Moreover, from the thermal variations of the dynamic total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types. - Highlights: • Dynamic behaviors of mixed spin HIN system are obtained within the EFT. • The system exhibits i, p and nm fundamental phases. • The dynamic phase diagrams are presented in (h, T), (D, T), (Δ S , T) and (r, T) planes. • The dynamic phase diagrams exhibit the dynamic tricritical point (TCP). • Different dynamic compensation types are obtained
Inverse freezing in the Hopfield fermionic Ising spin glass with a transverse magnetic field
International Nuclear Information System (INIS)
Morais, C.V.; Zimmer, F.M.; Magalhaes, S.G.
2011-01-01
The Hopfield fermionic Ising spin glass (HFISG) model in the presence of a magnetic transverse field Γ is used to study the inverse freezing transition. The mean field solution of this model allows introducing a parameter a that controls the frustration level. Particularly, in the present fermionic formalism, the chemical potential μ and the Γ provide a magnetic dilution and quantum spin flip mechanism, respectively. Within the one step replica symmetry solution and the static approximation, the results show that the reentrant transition between the spin glass and the paramagnetic phases, which is related to the inverse freezing for a certain range of μ, is gradually suppressed when the level of frustration a is decreased. Nevertheless, the quantum fluctuations caused by Γ can destroy this inverse freezing for any value of a.
Localized endomorphisms of the chiral Ising model
International Nuclear Information System (INIS)
Boeckenhauer, J.
1994-07-01
In the frame of the treatment of the chiral Ising model by Mack and Schomerus, examples of localized endomorphisms ρ 1 loc and ρ 1/2 loc are presented. It is shown that they lead to the same superselection sectors as the global ones in the sense that π 0 oρ 1 log ≅π 1 and π 0 pρ 1/2 loc ≅π 1/2 holds. For proving the latter unitary equivalence, Arakis formalism of the selfdual CAR algebra is used. Further it is shown that the localized endomorphisms obey the Ising fusion rules. (orig.)
Dynamical quantum phase transitions in extended transverse Ising models
Bhattacharjee, Sourav; Dutta, Amit
2018-04-01
We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with an additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model, where different quantum phases are characterized by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate, thereby leading to a single critical time scale for a given sector of Fisher zeros.
Computational Analysis of 3D Ising Model Using Metropolis Algorithms
International Nuclear Information System (INIS)
Sonsin, A F; Cortes, M R; Nunes, D R; Gomes, J V; Costa, R S
2015-01-01
We simulate the Ising Model with the Monte Carlo method and use the algorithms of Metropolis to update the distribution of spins. We found that, in the specific case of the three-dimensional Ising Model, methods of Metropolis are efficient. Studying the system near the point of phase transition, we observe that the magnetization goes to zero. In our simulations we analyzed the behavior of the magnetization and magnetic susceptibility to verify the phase transition in a paramagnetic to ferromagnetic material. The behavior of the magnetization and of the magnetic susceptibility as a function of the temperature suggest a phase transition around KT/J ≈ 4.5 and was evidenced the problem of finite size of the lattice to work with large lattice. (paper)
On the phase transition nature in compressible Ising models
International Nuclear Information System (INIS)
Ota, A.T.
1985-01-01
The phase transition phenomenon is analysed in a compressible ferromagnetic Ising model at null field, through the mean-field approximation. The model studied is d-dimensional under the magnetic point of view and one-dimensional under the elastic point of view. This is achieved keeping the compressive interactions among the ions and rejecting annealing forces completely. The exchange parameter J is linear and the elastic potential quadratic in relation to the microscopic shifts of the lattice. In the one-dimensional case, this model shows no phase transition. In the two-dimensional case, the role of the S i spin of the i-the ion is crucial: a) for spin 1/2 the transitions are of second order; b) for spin 1, desides the second order transitions there is a three-critical point and a first-order transitions line. (L.C.) [pt
Ising tricriticality in the extended Hubbard model with bond dimerization
Fehske, Holger; Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.
We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results. This work was supported by Deutsche Forschungsgemeinschaft (Germany), SFB 652, project B5, and by the EPSRC under Grant No. EP/N01930X/1 (FHLE).
Linear perturbation renormalization group method for Ising-like spin systems
Directory of Open Access Journals (Sweden)
J. Sznajd
2013-03-01
Full Text Available The linear perturbation group transformation (LPRG is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs1-xSex, UPd2Si2 or UNi2Si2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J121-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT2Si2 (T=Pd, Ni this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J2/J1 around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase.
Effects of the amorphization on hysteresis loops of the amorphous spin-1/2 Ising system
International Nuclear Information System (INIS)
Essaoudi, I.; Ainane, A.; Saber, M.; Miguel, J.J. de
2009-01-01
We examine the effects of the amorphization on the hysteresis loops of the amorphous spin-1/2 Ising system using the effective field theory within a probability distribution technique that accounts for the self-spin correlation functions. The magnetization, the transverse and longitudinal susceptibilities, and pyromagnetic coefficient are also studied in detail
The effective-field study of a mixed spin-1 and spin-5/2 Ising ferrimagnetic system
International Nuclear Information System (INIS)
Deviren, Bayram; Bati, Mehmet; Keskin, Mustafa
2009-01-01
An effective-field theory with correlations is developed for a mixed spin-1 and spin-5/2 Ising ferrimagnetic system on the honeycomb (δ=3) and square (δ=4) lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice magnetizations, and present the phase diagrams in the (Δ/|J|,k B T/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.
The effective-field study of a mixed spin-1 and spin-5/2 Ising ferrimagnetic system
Energy Technology Data Exchange (ETDEWEB)
Deviren, Bayram; Bati, Mehmet [Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr
2009-06-15
An effective-field theory with correlations is developed for a mixed spin-1 and spin-5/2 Ising ferrimagnetic system on the honeycomb ({delta}=3) and square ({delta}=4) lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction ({delta}) plane. We also investigate the thermal variations of the sublattice magnetizations, and present the phase diagrams in the ({delta}/|J|,k{sub B}T/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.
Monte Carlo technique for very large ising models
Kalle, C.; Winkelmann, V.
1982-08-01
Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetization M at T=1.4* T c is found to decay asymptotically as exp(-t/2.90) if t is measured in Monte Carlo steps per spin, and M( t = 0) = 1 initially.
Decorated Ising models with competing interactions and modulated structures
International Nuclear Information System (INIS)
Tragtenberg, M.H.R.; Yokoi, C.S.O.; Salinas, S.R.A.
1988-01-01
The phase diagrams of a variety of decorated Ising lattices are calculated. The competing interactions among the decorating spins may induce different types of modulated orderings. In particular, the effect of an applied field on the phase diagram of the two-dimensional mock ANNNI model is considered, where only the original horizontal bonds on a square lattice are decorated. Some Bravais lattices and Cayley trees where all bonds are equally decorated are then studied. The Bravais lattices display a few stable modulated structures. The Cayley trees, on the other hand, display a large number of modulated phases, which increases with the lattice coordination number. (authors) [pt
Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa
2017-10-01
The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.
International Nuclear Information System (INIS)
Keskin, Mustafa; Polat, Yasin
2009-01-01
The phase diagrams of the nonequilibrium mixed spin-3/2 and spin-2 Ising ferrimagnetic system on square lattice under a time-dependent external magnetic field are presented by using the Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices of spins σ=3/2 and S=2, and we take only nearest-neighbor interactions between pairs of spins. The system is in contact with a heat bath at absolute temperature T abs and the exchange of energy with the heat bath occurs via one-spin flip of the Glauber dynamics. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first- or second-order) phase transitions. The dynamic phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p), ferrimagnetic (i 1 , i 2 , i 3 ) phases, and three coexistence or mixed phase regions, namely i 1 +p, i 2 +p and i 3 +p mixed phases that strongly depend on interaction parameters.
Energy Technology Data Exchange (ETDEWEB)
Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr; Polat, Yasin [Institutes of Science, Erciyes University, 38039 Kayseri (Turkey)
2009-12-15
The phase diagrams of the nonequilibrium mixed spin-3/2 and spin-2 Ising ferrimagnetic system on square lattice under a time-dependent external magnetic field are presented by using the Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices of spins {sigma}=3/2 and S=2, and we take only nearest-neighbor interactions between pairs of spins. The system is in contact with a heat bath at absolute temperature T{sub abs} and the exchange of energy with the heat bath occurs via one-spin flip of the Glauber dynamics. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first- or second-order) phase transitions. The dynamic phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p), ferrimagnetic (i{sub 1}, i{sub 2}, i{sub 3}) phases, and three coexistence or mixed phase regions, namely i{sub 1}+p, i{sub 2}+p and i{sub 3}+p mixed phases that strongly depend on interaction parameters.
International Nuclear Information System (INIS)
Alécio, Raphael C.; Lyra, Marcelo L.; Strečka, Jozef
2016-01-01
The ground-state phase diagram, magnetization process and bipartite entanglement of the frustrated spin-1/2 Ising-Heisenberg and Heisenberg triangular tube (three-leg ladder) are investigated in a non-zero external magnetic field. The exact ground-state phase diagram of the spin-1/2 Ising-Heisenberg tube with Heisenberg intra-rung and Ising inter-rung couplings consists of six distinct gapped phases, which manifest themselves in a magnetization curve as intermediate plateaus at zero, one-third and two-thirds of the saturation magnetization. Four out of six available ground states exhibit quantum entanglement between two spins from the same triangular unit evidenced by a non-zero concurrence. Density-matrix renormalization group calculations are used in order to construct the ground-state phase diagram of the analogous but purely quantum spin-1/2 Heisenberg tube with Heisenberg intra- and inter-rung couplings, which consists of four gapped and three gapless phases. The Heisenberg tube shows a continuous change of the magnetization instead of a plateau at zero magnetization, while the intermediate one-third and two-thirds plateaus may be present or not in the zero-temperature magnetization curve. - Highlights: • Ground-state properties of Ising-Heisenberg and full Heisenberg spin tubes are studied. • Phases with 1/3 and 2/3 magnetization plateaus are present in both models. • We unveil the region in the parameter space on which inter-rung quantum fluctuations are relevant. • The full Heisenberg tube exhibits quantum bipartite entanglement between intra- as well as inter-rung spins.
Correlation functions of the Ising model and the eight-vertex model
International Nuclear Information System (INIS)
Ko, L.F.
1986-01-01
Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. In Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations
The Ising model and its applications to a phase transition of biological interest
International Nuclear Information System (INIS)
Cabrera, G.G.; Stein-Barana, A.M.; Zuckermann, M.J.
1984-01-01
It is investigated a gel-liquid crystal phase transition employing a two-state model equivalent to the Spin 1/2 Ising Model with applied magnetic field. The model is studied from the standpoint of the cluster variational method of Kikuchi for cooperative phenomena. (M.W.O.) [pt
Stable, metastable and unstable solutions of a spin-1 Ising system based on the free energy surfaces
Keskİin, Mustafa; Özgan, Şükrü
1990-04-01
Stable, metastable and unstable solutions of a spin-1 Ising model with bilinear and biquadratic interactions are found by using the free energy surfaces. The free energy expression is obtained in the lowest approximation of the cluster variation method. All these solutions are shown in the two-dimensional phase space, especially the unstable solutions which in some cases are difficult to illustrate in the two-dimensional phase space, found by Keskin et al. recently.
International Nuclear Information System (INIS)
Čisárová, Jana; Strečka, Jozef
2014-01-01
Exact solution of a coupled spin–electron linear chain composed of localized Ising spins and mobile electrons is found. The investigated spin–electron model is exactly solvable by the use of a transfer-matrix method after tracing out the degrees of freedom of mobile electrons delocalized over a couple of interstitial (decorating) sites. The exact ground-state phase diagram reveals an existence of five phases with different number of mobile electrons per unit cell, two of which are ferromagnetic, two are paramagnetic and one is antiferromagnetic. We have studied in particular the dependencies of compressibility and specific heat on temperature and electron density. - Highlights: • A coupled spin–electron chain composed of Ising spins and mobile electrons is exactly solved. • Quantum paramagnetic, ferromagnetic and antiferromagnetic ground states are found. • A compressibility shows a non-monotonous dependence on temperature and electron density. • Thermal dependences of specific heat display two distinct peaks
Search for the non-canonical Ising spin glass on rewired square lattices
Surungan, Tasrief
2018-03-01
A spin glass (SG) of non-canonical type is a purely antiferromagnetic (AF) system, exemplified by the AF Ising model on a scale free network (SFN), studied by Bartolozzi et al. [ Phys. Rev. B73, 224419 (2006)]. Frustration in this new type of SG is rendered by topological factor and its randomness is caused by random connectivity. As an SFN corresponds to a large dimensional lattice, finding non-canonical SG in lattice with physical dimension is desireable. However, a regular lattice can not have random connectivity. In order to obtain lattices with random connection and preserving the notion of finite dimension, we costructed rewired lattices. We added some extra bonds randomly connecting each site of a regular lattice to its next-nearest neighbors. Very recently, Surungan et al., studied AF Heisenberg system on rewired square lattice and found no SG behavior [AIP Conf. Proc. 1719, 030006 (2016)]. Due to the importance of discrete symmetry for phase transition, here we study similar structure for the Ising model (Z 2 symmetry). We used Monte Carlo simulation with Replica Exchange algorithm. Two types of structures were studied, firstly, the rewired square lattices with one extra bonds added to each site, and secondly, two bonds added to each site. We calculated the Edwards-Anderson paremeter, the commonly used parameter in searching for SG phase. The non-canonical SG is clearly observed in the rewired square lattice with two extra bonds added.
Relaxation theory of spin-3/2 Ising system near phase transition temperatures
International Nuclear Information System (INIS)
Canko, Osman; Keskin, Mustafa
2010-01-01
Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement. (general)
Tricritical Ising model with a boundary
International Nuclear Information System (INIS)
De Martino, A.; Moriconi, M.
1998-03-01
We study the integrable and supersymmetric massive φ (1,3) deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary S-matrices, which turn out to depend explicitly on the topological charge of the supersymmetry algebra. We also solve the general boundary Yang-Baxter equation and show that in appropriate limits the general reflection matrices go over the supersymmetry preserving solutions. Finally, we briefly discuss the possible connection between our reflection matrices and boundary perturbations within the framework of perturbed boundary conformal field theory. (author)
Exact solutions to plaquette Ising models with free and periodic boundaries
International Nuclear Information System (INIS)
Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard
2017-01-01
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) , who later dubbed it the fuki-nuke, or “no-ceiling”, model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) . We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Magnetoanisotropic spin-triplet Andreev reflection in ferromagnet-Ising superconductor junctions
Lv, Peng; Zhou, Yan-Feng; Yang, Ning-Xuan; Sun, Qing-Feng
2018-04-01
We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combining the nonequilibrium Green's function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is π instead of 2 π as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising superconductor. Furthermore, the dependence of the Andreev reflection on the incident energy and incident angle are also investigated. A complete Andreev reflection can occur when the incident energy is equal to the superconducting gap, regardless of the Fermi energy (spin polarization) of the ferromagnet. For the suitable oblique incidence, the spin-triplet Andreev reflection can be strongly enhanced. In addition, the conductance spectroscopies of both zero bias and finite bias are studied, and the influence of gate voltage, exchange energy, and spin-orbit coupling on the conductance spectroscopy are discussed in detail. The conductance exhibits a strong magnetoanisotropy with period π as the Andreev reflection coefficient. When the magnetization direction is parallel to the junction plane, a large conductance peak always emerges at the superconducting gap. This work offers a comprehensive and systematic study of the spin-triplet Andreev reflection and has an underlying application of π -periodic spin valve in spintronics.
Diluted Ising spin 1/2 lattice with an arbitrary coordination number
International Nuclear Information System (INIS)
Bach Thanh Cong; El Amraoui, Y.
1993-01-01
A useful representation for the Callen identity in the case of spin 1/2 is introduced by a simple technique. The phase diagrams, percolation problems of the diluted Ising lattice with arbitrary coordination number z are also discussed. (author). 12 refs, 5 figs
Form factors of Ising spin and disorder fields on the Poincare disc
International Nuclear Information System (INIS)
Doyon, Benjamin
2004-01-01
Using recent results concerning form factors of certain scaling fields in the massive Dirac theory on the Poincare disc, we find expressions for the form factors of Ising spin and disorder fields in the massive Majorana theory on the Poincare disc. In particular, we verify that these recent results agree with the factorization properties of the fields in the Dirac theory representing tensor products of spin and of disorder fields in the Majorana theory
The order parameters of a spin-1 Ising film in a transverse field
International Nuclear Information System (INIS)
Saber, A.; Ainane, A.; Dujardin, F.; Saber, M.; Stebe, B.
1998-08-01
Using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions, the layer longitudinal magnetizations and quadrupolar moments of a spin-1 Ising film and their averages are examined. These quantities as functions of the temperature, the ratio of the surface exchange interactions to the bulk ones, the strength of the transverse field and the film thickness are calculated numerically and some interesting results are obtained. (author)
Energy Technology Data Exchange (ETDEWEB)
Vatansever, Erol [Dokuz Eylül University, Graduate School of Natural and Applied Sciences, TR-35160 Izmir (Turkey); Polat, Hamza, E-mail: hamza.polat@deu.edu.tr [Department of Physics, Dokuz Eylül University, TR-35160 Izmir (Turkey)
2015-10-15
Nonequilibrium phase transition properties of a mixed Ising ferrimagnetic model consisting of spin-1/2 and spin-3/2 on a square lattice under the existence of a time dependent oscillating magnetic field have been investigated by making use of Monte Carlo simulations with a single-spin flip Metropolis algorithm. A complete picture of dynamic phase boundary and magnetization profiles have been illustrated and the conditions of a dynamic compensation behavior have been discussed in detail. According to our simulation results, the considered system does not point out a dynamic compensation behavior, when it only includes the nearest-neighbor interaction, single-ion anisotropy and an oscillating magnetic field source. As the next-nearest-neighbor interaction between the spins-1/2 takes into account and exceeds a characteristic value which sensitively depends upon values of single-ion anisotropy and only of amplitude of external magnetic field, a dynamic compensation behavior occurs in the system. Finally, it is reported that it has not been found any evidence of dynamically first-order phase transition between dynamically ordered and disordered phases, which conflicts with the recently published molecular field investigation, for a wide range of selected system parameters. - Highlights: • Spin-1/2 and spin-3/2 Ising ferrimagnetic model is examined. • The system is exposed to time-dependent magnetic field. • Kinetic Monte Carlo simulation technique is used. • Any evidence of first-order phase transition has not been found.
Dynamics of the Random Field Ising Model
Xu, Jian
The Random Field Ising Model (RFIM) is a general tool to study disordered systems. Crackling noise is generated when disordered systems are driven by external forces, spanning a broad range of sizes. Systems with different microscopic structures such as disordered mag- nets and Earth's crust have been studied under the RFIM. In this thesis, we investigated the domain dynamics and critical behavior in two dipole-coupled Ising ferromagnets Nd2Fe14B and LiHoxY 1-xF4. With Tc well above room temperature, Nd2Fe14B has shown reversible disorder when exposed to an external transverse field and crosses between two universality classes in the strong and weak disorder limits. Besides tunable disorder, LiHoxY1-xF4 has shown quantum tunneling effects arising from quantum fluctuations, providing another mechanism for domain reversal. Universality within and beyond power law dependence on avalanche size and energy were studied in LiHo0.65Y0.35 F4.
Lifshitz-Allen-Cahn domain-growth kinetics of Ising models with conserved density
DEFF Research Database (Denmark)
Fogedby, Hans C.; Mouritsen, Ole G.
1988-01-01
The domain-growth kinetics of p=fourfold degenerate (2×1) ordering in two-dimensional Ising models with conserved density is studied as a function of temperature and range of Kawasaki spin exchange. It is found by computer simulations that the zero-temperature freezing-in behavior for nearest-nei...
Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain
Directory of Open Access Journals (Sweden)
L. Čanová
2009-01-01
Full Text Available The geometric frustration in a class of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chains is investigated by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. The ground state, the magnetization process and the specific heat as a function of the external magnetic field are particularly examined for different strengths of the geometric frustration. It is shown that the increase of the Heisenberg spin value S raises the number of intermediate magnetization plateaux, which emerge in magnetization curves provided that the ground state is highly degenerate on behalf of a sufficiently strong geometric frustration. On the other hand, all intermediate magnetization plateaux merge into a linear magnetization versus magnetic field dependence in the limit of classical Heisenberg spin S → ∞. The enhanced magnetocaloric effect with cooling rate exceeding the one of paramagnetic salts is also detected when the disordered frustrated phase constitutes the ground state and the external magnetic field is small enough.
International Nuclear Information System (INIS)
Bachschmid-Romano, Ludovica; Opper, Manfred
2015-01-01
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the nontrivial equal time correlations between spins induced by the dynamics for the speed of learning. These correlations become more important as the spin’s stochasticity is decreased. We also analyse the deviation of the estimation error (paper)
International Nuclear Information System (INIS)
Bobak, A.; Dely, J.
2007-01-01
The effect of a single-ion anisotropy on the phase diagram of the mixed spin-32 and spin-2 Ising system is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the free energy. Topologically different kinds of phase diagrams are achieved by changing values of the parameter in the model Hamiltonian. Besides second-order transitions, lines of first-order transitions terminating either at a tricritical point or an isolated critical point, are found
A fully programmable 100-spin coherent Ising machine with all-to-all connections
McMahon, Peter; Marandi, Alireza; Haribara, Yoshitaka; Hamerly, Ryan; Langrock, Carsten; Tamate, Shuhei; Inagaki, Takahiro; Takesue, Hiroki; Utsunomiya, Shoko; Aihara, Kazuyuki; Byer, Robert; Fejer, Martin; Mabuchi, Hideo; Yamamoto, Yoshihisa
We present a scalable optical processor with electronic feedback, based on networks of optical parametric oscillators. The design of our machine is inspired by adiabatic quantum computers, although it is not an AQC itself. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections. This research was funded by the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) Program of the Council of Science, Technology and Innovation (Cabinet Office, Government of Japan).
Complex-network description of thermal quantum states in the Ising spin chain
Sundar, Bhuvanesh; Valdez, Marc Andrew; Carr, Lincoln D.; Hazzard, Kaden R. A.
2018-05-01
We use network analysis to describe and characterize an archetypal quantum system—an Ising spin chain in a transverse magnetic field. We analyze weighted networks for this quantum system, with link weights given by various measures of spin-spin correlations such as the von Neumann and Rényi mutual information, concurrence, and negativity. We analytically calculate the spin-spin correlations in the system at an arbitrary temperature by mapping the Ising spin chain to fermions, as well as numerically calculate the correlations in the ground state using matrix product state methods, and then analyze the resulting networks using a variety of network measures. We demonstrate that the network measures show some traits of complex networks already in this spin chain, arguably the simplest quantum many-body system. The network measures give insight into the phase diagram not easily captured by more typical quantities, such as the order parameter or correlation length. For example, the network structure varies with transverse field and temperature, and the structure in the quantum critical fan is different from the ordered and disordered phases.
Pereira, J. R. V.; Tunes, T. M.; de Arruda, A. S.; Godoy, M.
2018-06-01
In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins SA = 1 in the sublattice A and SB = 3 / 2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J single-ion anisotropies, DiA and DjB , on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature Tc versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution.
Ferromagnetic transitions of a spin-one Ising film in a surface and bulk transverse fields
International Nuclear Information System (INIS)
Saber, A.; Lo Russo, S.; Mattei, G.; Mattoni, A.
2002-01-01
Using the effective field theory method, we have calculated the Curie temperature of a spin-one Ising ferromagnetic film in a surface and bulk transverse fields. Numerical calculations give phase diagrams under various parameters. Surface exchange enhancement is considered. The dependence of the critical transverse field on film thickness, and phase diagrams in the fields, critical surface transverse field versus the bulk one are presented
The Peierls argument for higher dimensional Ising models
International Nuclear Information System (INIS)
Bonati, Claudio
2014-01-01
The Peierls argument is a mathematically rigorous and intuitive method to show the presence of a non-vanishing spontaneous magnetization in some lattice models. This argument is typically explained for the D = 2 Ising model in a way which cannot be easily generalized to higher dimensions. The aim of this paper is to present an elementary discussion of the Peierls argument for the general D-dimensional Ising model. (paper)
International Nuclear Information System (INIS)
Keskin, Mustafa; Canko, Osman
2005-01-01
The relaxation behavior of the spin-3/2 Ising model Hamiltonian with bilinear and biquadratic interactions near the second-order phase transition temperature or critical temperature is studied by means of the Onsager's theory of irreversible thermodynamics or the Onsager reciprocity theorem (ORT). First, we give the equilibrium case briefly within the molecular-field approximation in order to study the relaxation behavior by using the ORT. Then, the ORT is applied to the model and the kinetic equations are obtained. By solving these equations, three relaxation times are calculated and examined for temperatures near the second-order phase transition temperature. It is found that one of the relaxation times goes to infinity near the critical temperature on either side, the second relaxation time makes a cusp at the critical temperature and third one behaves very differently in which it terminates at the critical temperature while approaching it, then showing a 'flatness' property and then decreases. We also study the influences of the Onsager rate coefficients on the relaxation times. The behavior of these relaxation times is discussed and compared with the spin-1/2 and spin-1 Ising systems
Ising formulation of associative memory models and quantum annealing recall
Santra, Siddhartha; Shehab, Omar; Balu, Radhakrishnan
2017-12-01
Associative memory models, in theoretical neuro- and computer sciences, can generally store at most a linear number of memories. Recalling memories in these models can be understood as retrieval of the energy minimizing configuration of classical Ising spins, closest in Hamming distance to an imperfect input memory, where the energy landscape is determined by the set of stored memories. We present an Ising formulation for associative memory models and consider the problem of memory recall using quantum annealing. We show that allowing for input-dependent energy landscapes allows storage of up to an exponential number of memories (in terms of the number of neurons). Further, we show how quantum annealing may naturally be used for recall tasks in such input-dependent energy landscapes, although the recall time may increase with the number of stored memories. Theoretically, we obtain the radius of attractor basins R (N ) and the capacity C (N ) of such a scheme and their tradeoffs. Our calculations establish that for randomly chosen memories the capacity of our model using the Hebbian learning rule as a function of problem size can be expressed as C (N ) =O (eC1N) , C1≥0 , and succeeds on randomly chosen memory sets with a probability of (1 -e-C2N) , C2≥0 with C1+C2=(0.5-f ) 2/(1 -f ) , where f =R (N )/N , 0 ≤f ≤0.5 , is the radius of attraction in terms of the Hamming distance of an input probe from a stored memory as a fraction of the problem size. We demonstrate the application of this scheme on a programmable quantum annealing device, the D-wave processor.
Particles and scaling for lattice fields and Ising models
International Nuclear Information System (INIS)
Glimm, J.; Jaffe, A.
1976-01-01
The conjectured inequality GAMMA 6 4 -fields and the scaling limit for d-dimensional Ising models. Assuming GAMMA 6 = 6 these phi 4 fields are free fields unless the field strength renormalization Z -1 diverges. (orig./BJ) [de
The ising model on the dynamical triangulated random surface
International Nuclear Information System (INIS)
Aleinov, I.D.; Migelal, A.A.; Zmushkow, U.V.
1990-01-01
The critical properties of Ising model on the dynamical triangulated random surface embedded in D-dimensional Euclidean space are investigated. The strong coupling expansion method is used. The transition to thermodynamical limit is performed by means of continuous fractions
International Nuclear Information System (INIS)
Ertas, Mehmet; Keskin, Mustafa; Deviren, Bayram
2010-01-01
The dynamic phase transitions are studied in the spin-2 Ising model under a time-dependent oscillating magnetic field by using the effective-field theory with correlations. The effective-field dynamic equation is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic order parameter and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are presented in (T/zJ, h/zJ) plane.
The ferromagnet spin-1/2 Ising superlattice in a transverse field
International Nuclear Information System (INIS)
Bouziane, T.; Saber, M.; Belaaraj, A.; Ainane, A.
1998-09-01
The phase transitions of a ferromagnet spin-1/2 Ising superlattice consisting of two different materials in a transverse field is examined with the use of effective field theory that accounts for the self-spin function correlation. The critical temperature of the system is studied as a function of the thickness of the constituents in a unit cell and of exchange interactions in each material. A critical interface exchange interaction above which the interface magnetism appears is found. The effects of a uniform transverse field and the interface exchange interaction on the parameters of the system are also investigated. (author)
The phase diagrams of the site-diluted spin-1/2 Ising superlattice
International Nuclear Information System (INIS)
Saber, A.; Essaoudi, I.; Ainane, A.; Dujardin, F.; Saber, M.; Stebe, B.
1998-08-01
Using the effective field theory with a probability distribution technique that accounts for the single-site spin correlations, the critical behavior of a diluted spin-1/2 Ising superlattice consisting of two different ferromagnet materials is examined. The critical temperature of the system is studied as a function of the thickness of the constituents in a unit cell, the concentration of magnetic atoms, and the exchange interactions in each material. It is shown that the properties of the diluted system are different from those of the corresponding pure system. (author)
Quantum Ising model on hierarchical structures
International Nuclear Information System (INIS)
Lin Zhifang; Tao Ruibao.
1989-11-01
A quantum Ising chain with both the exchange couplings and the transverse fields arranged in a hierarchical way is considered. Exact analytical results for the critical line and energy gap are obtained. It is shown that when R 1 not= R 2 , where R 1 and R 2 are the hierarchical parameters for the exchange couplings and the transverse fields, respectively, the system undergoes a phase transition in a different universality class from the pure quantum Ising chain with R 1 =R 2 =1. On the other hand, when R 1 =R 2 =R, there exists a critical value R c dependent on the furcating number of the hierarchy. In case of R > R c , the system is shown to exhibit as Ising-like critical point with the critical behaviour the same as in the pure case, while for R c the system belongs to another universality class. (author). 19 refs, 2 figs
Dynamics of the two-dimensional directed Ising model in the paramagnetic phase
Godrèche, C.; Pleimling, M.
2014-05-01
We consider the nonconserved dynamics of the Ising model on the two-dimensional square lattice, where each spin is influenced preferentially by its east and north neighbours. The single-spin flip rates are such that the stationary state is Gibbsian with respect to the usual ferromagnetic Ising Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical transition between two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite, when the asymmetry parameter is less than a threshold value, and a regime of strong violation where this ratio vanishes asymptotically above the threshold. This study suggests that this novel kind of dynamical transition in nonequilibrium stationary states, already found for the directed Ising chain and the spherical model with asymmetric dynamics, might be quite general. In contrast with the latter models, the equal-time correlation function for the two-dimensional directed Ising model depends on the asymmetry.
Singh, R. R. P.; Young, A. P.
2017-12-01
We discuss generation of series expansions for Ising spin glasses with a symmetric ±J (i.e., bimodal) distribution on d -dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problems, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field h , for which we obtain high temperature series expansions in variables tanh(J /T ) and tanh(h /T ) . The quantum problem is a T =0 study of the Ising spin glass in a transverse magnetic field hT for which we obtain a perturbation theory in powers of J /hT . These methods require (i) enumeration and counting of all connected clusters that can be embedded in the lattice up to some order n , and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order n and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the ±J bonds and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the T =0 quantum system. Details of the calculational methods are presented.
Two dimensional kicked quantum Ising model: dynamical phase transitions
International Nuclear Information System (INIS)
Pineda, C; Prosen, T; Villaseñor, E
2014-01-01
Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality. (paper)
Effective field study of ising model on a double perovskite structure
Energy Technology Data Exchange (ETDEWEB)
Ngantso, G. Dimitri; El Amraoui, Y. [LMPHE, (URAC 12), Faculté des Sciences, Université Mohammed V, Rabat (Morocco); Benyoussef, A. [LMPHE, (URAC 12), Faculté des Sciences, Université Mohammed V, Rabat (Morocco); Center of Materials and Nanomaterials, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); El Kenz, A., E-mail: elkenz@fsr.ac.ma [LMPHE, (URAC 12), Faculté des Sciences, Université Mohammed V, Rabat (Morocco)
2017-02-01
By using the effective field theory (EFT), the mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model adapted to a double perovskite structure has been studied. The EFT calculations have been carried out from Ising Hamiltonian by taking into account first and second nearest-neighbors interactions and the crystal and external magnetic fields. Both first- and second-order phase transitions have been found in phase diagrams of interest. Depending on crystal-field values, the thermodynamic behavior of total magnetization indicated the compensation phenomenon existence. The hysteresis behaviors are studied by investigating the reduced magnetic field dependence of total magnetization and a series of hysteresis loops are shown for different reduced temperatures around the critical one. - Highlights: • Magnetic properties of double perovskite Structure have been studied. • Compensation temperature has been observed below the critical temperature. • Hysteresis behaviors have been studied.
Effective field study of ising model on a double perovskite structure
International Nuclear Information System (INIS)
Ngantso, G. Dimitri; El Amraoui, Y.; Benyoussef, A.; El Kenz, A.
2017-01-01
By using the effective field theory (EFT), the mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model adapted to a double perovskite structure has been studied. The EFT calculations have been carried out from Ising Hamiltonian by taking into account first and second nearest-neighbors interactions and the crystal and external magnetic fields. Both first- and second-order phase transitions have been found in phase diagrams of interest. Depending on crystal-field values, the thermodynamic behavior of total magnetization indicated the compensation phenomenon existence. The hysteresis behaviors are studied by investigating the reduced magnetic field dependence of total magnetization and a series of hysteresis loops are shown for different reduced temperatures around the critical one. - Highlights: • Magnetic properties of double perovskite Structure have been studied. • Compensation temperature has been observed below the critical temperature. • Hysteresis behaviors have been studied.
Boson-mediated quantum spin simulators in transverse fields: X Y model and spin-boson entanglement
Wall, Michael L.; Safavi-Naini, Arghavan; Rey, Ana Maria
2017-01-01
The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an X Y model by off-resonant driving of a single sideband of boson excitation (i.e., a single-beam Mølmer-Sørensen scheme) and a boson-mediated Ising simulator in the presence of a transverse field. In particular, we show that these two schemes have the same effective Hamiltonian in suitably defined rotating frames, and analyze the emergent effective X Y spin model through a truncated Magnus series and numerical simulations. In addition to X Y spin-spin interactions that can be nonperturbatively renormalized from the naive Ising spin-spin coupling constants, we find an effective transverse field that is dependent on the thermal energy of the bosons, as well as other spin-boson couplings that cause spin-boson entanglement not to vanish at any time. In the case of a boson-mediated Ising simulator with transverse field, we discuss the crossover from transverse field Ising-like to X Y -like spin behavior as a function of field strength.
Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles with core–shell structure
International Nuclear Information System (INIS)
Deviren, Bayram; Şener, Yunus
2015-01-01
The magnetic properties of mixed spin-1 and spin-3/2 Ising nanoparticles with core/shell structure are studied by using the effective-field theory with correlations. We investigate the thermal variations of the core, shell and total magnetizations and the Q-, R-, P-, S-, N- and L-types of compensation behavior in Néel classification nomenclature exists in the system. The effects of the crystal-field, core and shell interactions and interface coupling, on the phase diagrams are investigated in detail and the obtained phase diagrams are presented in three different planes. The system exhibits both second- and first-order phase transitions besides tricritical point, double critical end point, triple point and critical end point depending on the appropriate values of the interaction parameters. The system strongly affected by the surface situations and some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. - Highlights: • Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles are investigated. • The system exhibits tricritical, double critical end, triple, critical end points. • Q-, R-, P-, S-, N- and L-types of compensation behavior are found. • Some characteristic phenomena are found depending on the interaction parameters. • Effects of crystal-field and bilinear interactions on the system are examined
Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles with core–shell structure
Energy Technology Data Exchange (ETDEWEB)
Deviren, Bayram, E-mail: bayram.deviren@nevsehir.edu.tr [Department of Physics, Nevsehir Hacı Bektaş Veli University, 50300 Nevşehir (Turkey); Şener, Yunus [Institute of Science, Department of Physics, Nevsehir Hacı Bektaş Veli University, 50300 Nevşehir (Turkey)
2015-07-15
The magnetic properties of mixed spin-1 and spin-3/2 Ising nanoparticles with core/shell structure are studied by using the effective-field theory with correlations. We investigate the thermal variations of the core, shell and total magnetizations and the Q-, R-, P-, S-, N- and L-types of compensation behavior in Néel classification nomenclature exists in the system. The effects of the crystal-field, core and shell interactions and interface coupling, on the phase diagrams are investigated in detail and the obtained phase diagrams are presented in three different planes. The system exhibits both second- and first-order phase transitions besides tricritical point, double critical end point, triple point and critical end point depending on the appropriate values of the interaction parameters. The system strongly affected by the surface situations and some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. - Highlights: • Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles are investigated. • The system exhibits tricritical, double critical end, triple, critical end points. • Q-, R-, P-, S-, N- and L-types of compensation behavior are found. • Some characteristic phenomena are found depending on the interaction parameters. • Effects of crystal-field and bilinear interactions on the system are examined.
International Nuclear Information System (INIS)
Deviren, Bayram; Kantar, Ersin; Keskin, Mustafa
2010-01-01
The magnetic properties of the ferrimagnetic mixed spin-3/2 and spin-2 Ising model with a crystal field in a longitudinal magnetic field on a honeycomb (δ = 3) and a square lattice (δ = 4) are studied by using the effective-field theory with correlations. The ground-state phase diagram of the model is obtained in a longitudinal magnetic field (h) for a single-ion potential or a crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice magnetization, and present the phase diagrams in the (Δ/|J|, k B T/|J|) plane. The susceptibility, internal energy, and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field. Moreover, the system undergoes first- and second-order phase transitions; hence, the system has a tricritical point. The system also exhibits reentrant behaviors.
Energy Technology Data Exchange (ETDEWEB)
Deviren, Bayram [Nevsehir University, Nevsehir (Turkmenistan); Kantar, Ersin; Keskin, Mustafa [Erciyes University, Kayseri (Turkmenistan)
2010-06-15
The magnetic properties of the ferrimagnetic mixed spin-3/2 and spin-2 Ising model with a crystal field in a longitudinal magnetic field on a honeycomb ({delta} = 3) and a square lattice ({delta} = 4) are studied by using the effective-field theory with correlations. The ground-state phase diagram of the model is obtained in a longitudinal magnetic field (h) for a single-ion potential or a crystal-field interaction ({Delta}) plane. We also investigate the thermal variations of the sublattice magnetization, and present the phase diagrams in the ({Delta}/|J|, k{sub B}T/|J|) plane. The susceptibility, internal energy, and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field. Moreover, the system undergoes first- and second-order phase transitions; hence, the system has a tricritical point. The system also exhibits reentrant behaviors.
The high-temperature expansion of the classical Ising model with Sz2 term
Directory of Open Access Journals (Sweden)
M.T. Thomaz
2012-03-01
Full Text Available We derive the high-temperature expansion of the Helmholtz free energy up to order β17 of the one-dimensional spin-S Ising model, with single-ion anisotropy term, in the presence of a longitudinal magnetic field. We show that the values of some thermodynamical functions for the ferromagnetic models, in the presence of a weak magnetic field, are not small corrections to their values with h=0. This model with S=3 was applied by Kishine et al. [J.-i. Kishine et al., Phys. Rev. B, 2006, 74, 224419] to analyze experimental data of the single-chain magnet [Mn (saltmen]2 [Ni(pac2 (py2] (PF62 for T<40 K. We show that for T<35 K the thermodynamic functions of the large-spin limit model are poor approximations to their analogous spin-3 functions.
Ising model on tangled chain - 2: Magnetization and susceptibility
International Nuclear Information System (INIS)
Mejdani, R.
1993-05-01
In the preceding paper we have considered an Ising model defined on tangled chain to study the behaviour of the free energy and entropy, particularly in the zero-field and zero-temperature limit. In this paper, following the main line and basing on some results of the previous work, we shall study in the ''language'' of state configurations the behaviour of the magnetization and the susceptibility for different conditions of the model, to understand better the competition between the ferromagnetic bonds along the chain and the antiferromagnetic additional bonds across the chain. Particularly interesting is the behaviour of the susceptibility in the zero-field and zero-temperature limit. Exact solutions for the magnetization and susceptibility, generated by analytical calculations and iterative algorithms, are described. The additional bonds, introduced as a form of perfectly disorder, indicate a particular effect on the spin correlation. We found that the condition J=-J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a ''transition-region'' condition for this behaviour. (author). 16 refs, 14 figs
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Bahmad, L. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco)
2015-09-01
The magnetic behaviors of a mixed spins (2-1) hexagonal Ising nanowire with core–shell structure are investigated by using the Monte Carlo simulations. The thermal magnetizations, the magnetic susceptibilities and the transition temperatures of core–shell are studied for different values of crystal field and exchange interactions. The thermal and magnetic hysteresis cycles are given for different values of the crystal field. - Highlights: • Critical temperature increase when exchange interaction increasing in core-shell. • Hysteresis loop areas decrease at above transition temperature. • Magnetic coercive field decrease when crystal field increasing. • Magnetic coercive field increase when exchange interaction increasing.
Tricriticality in the q-neighbor Ising model on a partially duplex clique.
Chmiel, Anna; Sienkiewicz, Julian; Sznajd-Weron, Katarzyna
2017-12-01
We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r^{*}(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears.
Zeros of the partition function for some generalized Ising models
International Nuclear Information System (INIS)
Dunlop, F.
1981-01-01
The author considers generalized Ising Models with two and four body interactions in a complex external field h such that Re h>=mod(Im h) + C, where C is an explicit function of the interaction parameters. The partition function Z(h) is then shown to satisfy mod(Z(h))>=Z(c), so that the pressure is analytic in h inside the given region. The method is applied to specific examples: the gauge invariant Ising Model, and the Widom Rowlinson model on the lattice. (Auth.)
Learning and inference in a nonequilibrium Ising model with hidden nodes.
Dunn, Benjamin; Roudi, Yasser
2013-02-01
We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.
Heat fluctuations in Ising models coupled with two different heat baths
Energy Technology Data Exchange (ETDEWEB)
Piscitelli, A; Gonnella, G [Dipartimento di Fisica, Universita di Bari and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Amendola 173, 70126 Bari (Italy); Corberi, F [Dipartimento di Matematica ed Informatica, via Ponte don Melillo, Universita di Salerno, 84084 Fisciano (Italy)
2008-08-22
Monte Carlo simulations of Ising models coupled to heat baths at two different temperatures are used to study a fluctuation relation for the heat exchanged between the two thermostats in a time {tau}. Different kinetics (single-spin-flip or spin-exchange Kawasaki dynamics), transition rates (Glauber or Metropolis), and couplings between the system and the thermostats have been considered. In every case the fluctuation relation is verified in the large {tau} limit, both in the disordered and in the low temperature phase. Finite-{tau} corrections are shown to obey a scaling behavior. (fast track communication)
Conformal Invariance in the Long-Range Ising Model
Paulos, Miguel F; van Rees, Balt C; Zan, Bernardo
2016-01-01
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Conformal invariance in the long-range Ising model
Directory of Open Access Journals (Sweden)
Miguel F. Paulos
2016-01-01
Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Conformal invariance in the long-range Ising model
Energy Technology Data Exchange (ETDEWEB)
Paulos, Miguel F. [CERN, Theory Group, Geneva (Switzerland); Rychkov, Slava, E-mail: slava.rychkov@lpt.ens.fr [CERN, Theory Group, Geneva (Switzerland); Laboratoire de Physique Théorique de l' École Normale Supérieure (LPTENS), Paris (France); Faculté de Physique, Université Pierre et Marie Curie (UPMC), Paris (France); Rees, Balt C. van [CERN, Theory Group, Geneva (Switzerland); Zan, Bernardo [Institute of Physics, Universiteit van Amsterdam, Amsterdam (Netherlands)
2016-01-15
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
New relation for critical exponents in the Ising model
International Nuclear Information System (INIS)
Pishtshev, A.
2007-01-01
The Ising model in a transverse field is considered at T=0. From the analysis of the power low behaviors of the energy gap and the order parameter as functions of the field a new relation between the respective critical exponents, β>=1/(8s 2 ), is derived. By using the Suzuki equivalence from this inequality a new relation for critical exponents in the Ising model, β>=1/(8ν 2 ), is obtained. A number of numerical examples for different cases illustrates the generality and validity of the relation. By applying this relation the estimation ν=(1/4) 1/3 ∼0.62996 for the 3D-Ising model is proposed
Phase diagrams of a spin-1 Ising superlattice with alternating transverse field
International Nuclear Information System (INIS)
Saber, A.; Ez-Zahraouy, H.; Lo Russo, S.; Mattei, G.; Ainane, A.
2003-01-01
The effects of alternating transverse fields Ω a and Ω b on the critical behavior of an alternating spin-1 Ising superlattice are studied within an effective field theory with a probability distribution technique that accounts for the single-site spin correlation. Critical temperatures are calculated as a function of the thickness of the superlattice and the strength of the transverse field. Depending on the values of the transverse fields Ω a and Ω b , the critical temperature can increase or decrease with increasing the thickness of the film, such result is not obtained in the uniform transverse field case (Ω a = Ω b ). Furthermore, for each thickness L of the film, a long range ordered phase persist at low temperature for selected values of the transverse field Ω a and arbitrary values of Ω b . The effects of interlayer and intralayer exchange interactions are also examined
Phase diagrams of a spin-1 Ising superlattice with alternating transverse field
International Nuclear Information System (INIS)
Saber, A.; Ez-Zahraouy, H.
2000-09-01
The effects of alternating transverse fields Ω a and Ω b on the critical behavior of an alternating spin-1 Ising superlattice are studied within an effective field theory with a probability distribution technique that accounts for the single-site spin correlations. Critical temperatures are calculated as a function of the thickness of the superlattice and the strength of the transverse field. Depending on the values of the transverse fields Ω a and Ω b , the critical temperature can increase or decrease with increasing the thickness of the film, such result is not obtained in the uniform transverse field case (Ω a = Ω b ). Furthermore, for each thickness L of the film, a long range ordered phase persists at low temperature for selected values of the transverse field Ω a and arbitrary values of Ω b . The effects of interlayer and intralayer exchange interactions are also examined. (author)
Mixed spin-((1)/(2)) and spin-1 Blume-Capel Ising ferrimagnetic system on the Bethe lattice
International Nuclear Information System (INIS)
Albayrak, Erhan; Keskin, Mustafa
2003-01-01
The mixed spin-((1)/(2)) and spin-1 Blume-Capel Ising ferrimagnetic system is studied on the Bethe lattice by using the exact recursion equations. Exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q=3, 4, 5 and 6. The existence of a tricritical point is investigated for different values of q. The results are compared with those of other approximate methods and with the exact result on the Bethe lattice by using a discrete nonlinear map and also the exact results that are available for the case of the honeycomb lattice
Quantum-information approach to the Ising model: Entanglement in chains of qubits
International Nuclear Information System (INIS)
Stelmachovic, Peter; Buzek, Vladimir
2004-01-01
Simple physical interactions between spin-1/2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin-1/2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin-1/2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter λ has a maximum around the point λ=1, and it monotonically decreases for large values of λ. We prove that in the limit λ→∞ this state is locally unitary equivalent to an N-partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the X-state). This X-state exhibits the 'extreme' entanglement in a sense that an arbitrary subset A of k≤n qubits in the Ising chain composed of N=2n+1 qubits is maximally entangled with the remaining qubits (set B) in the chain. In addition, we prove that by performing a local operation just on the subset B, one can transform the X-state into a direct product of k singlets shared by the parties A and B. This property of the X-state can be utilized for new secure multipartite communication protocols
Entanglement and quantum state geometry of a spin system with all-range Ising-type interaction
Kuzmak, A. R.
2018-04-01
The evolution of an N spin-1/2 system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the number of spins and the initial state. Also, the geometry of the manifold, which contains entangled states, is obtained. For this case we find the dependence of entanglement on the scalar curvature of the manifold and examine it for different numbers of spins in the system. Finally we show that the transverse magnetic field leads to a change in the manifold topology.
Quantum dynamics in transverse-field Ising models from classical networks
Directory of Open Access Journals (Sweden)
Markus Schmitt, Markus Heyl
2018-02-01
Full Text Available The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.
The square Ising model with second-neighbor interactions and the Ising chain in a transverse field
International Nuclear Information System (INIS)
Grynberg, M.D.; Tanatar, B.
1991-06-01
We consider the thermal and critical behaviour of the square Ising lattice with frustrated first - and second-neighbor interactions. A low-temperature domain wall analysis including kinks and dislocations shows that there is a close relation between this classical model and the Hamiltonian of an Ising chain in a transverse field provided that the ratio of the next-nearest to nearest-neighbor coupling, is close to 1/2. Due to the field inversion symmetry of the Ising chain Hamiltonian, the thermal properties of the classical system are symmetrical with respect to this coupling ratio. In the neighborhood of this regime critical exponents of the model turn out to belong to the Ising universality class. Our results are compared with previous Monte Carlo simulations. (author). 23 refs, 6 figs
Specific heat of the simple-cubic Ising model
Feng, X.; Blöte, H.W.J.
2010-01-01
We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
Monte Carlo method for critical systems in infinite volume: The planar Ising model.
Herdeiro, Victor; Doyon, Benjamin
2016-10-01
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.
Wang, Zhe; Lorenz, T.; Gorbunov, D. I.; Cong, P. T.; Kohama, Y.; Niesen, S.; Breunig, O.; Engelmayer, J.; Herman, A.; Wu, Jianda; Kindo, K.; Wosnitza, J.; Zherlitsyn, S.; Loidl, A.
2018-05-01
We report on magnetization, sound-velocity, and magnetocaloric-effect measurements of the Ising-like spin-1 /2 antiferromagnetic chain system BaCo2V2O8 as a function of temperature down to 1.3 K and an applied transverse magnetic field up to 60 T. While across the Néel temperature of TN˜5 K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature the field-dependent measurements reveal a sharp softening of sound velocity v (B ) and a clear minimum of temperature T (B ) at B⊥c,3 D=21.4 T , indicating the suppression of the antiferromagnetic order. At higher fields, the T (B ) curve shows a broad minimum at B⊥c=40 T , accompanied by a broad minimum in the sound velocity and a saturationlike magnetization. These features signal a quantum phase transition, which is further characterized by the divergent behavior of the Grüneisen parameter ΓB∝(B -B⊥c)-1. By contrast, around the critical field, the Grüneisen parameter converges as temperature decreases, pointing to a quantum critical point of the one-dimensional transverse-field Ising model.
Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models
Mitchell, S. J.; Landau, D. P.
2006-03-01
Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic (s=1/2) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems (512^2) and long times (10^ 6 MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of 1/3 [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.Supported by the NSF.[1] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, second ed. (Cambridge University Press, New York, 2005).[2] J. Amar, F. Sullivan, and R.D. Mountain, Phys. Rev. B 37, 196 (1988).
The cavity approach to parallel dynamics of Ising spins on a graph
International Nuclear Information System (INIS)
Neri, I; Bollé, D
2009-01-01
We use the cavity method to study the parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single-site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for the stationary distribution. We present the phase diagrams for an Ising model on an asymmetric Bethe lattice and for a neural network with Hebbian interactions on an asymmetric scale-free graph. For graphs with a nonzero fraction of symmetric edges the equations can be solved for a finite number of time steps. Theoretical predictions are confirmed by simulations. Using a heuristic method the cavity equations are extended to a set of equations that determine the marginals of the stationary distribution of Ising models on graphs with a nonzero fraction of symmetric edges. The results from this method are discussed and compared with simulations
Energy Technology Data Exchange (ETDEWEB)
Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr; Canko, Osman [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Kantar, Ersin [Institute of Science, Erciyes University, 38039 Kayseri (Turkey)
2009-06-15
We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.
International Nuclear Information System (INIS)
Keskin, Mustafa; Canko, Osman; Kantar, Ersin
2009-01-01
We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.
Sound dispersion in a spin-1 Ising system near the second-order phase transition point
International Nuclear Information System (INIS)
Erdem, Ryza; Keskin, Mustafa
2003-01-01
Sound dispersion relation is derived for a spin-1 Ising system and its behaviour near the second-order phase transition point or the critical point is analyzed. The method used is a combination of molecular field approximation and Onsager theory of irreversible thermodynamics. If we assume a linear coupling of sound wave with the order parameter fluctuations in the system, we find that the dispersion which is the relative sound velocity change with frequency behaves as ω 0 ε 0 , where ω is the sound frequency and ε the temperature distance from the critical point. In the ordered region, one also observes a frequency-dependent velocity or dispersion minimum which is shifted from the corresponding attenuation maxima. These phenomena are in good agreement with the calculations of sound velocity in other magnetic systems such as magnetic metals, magnetic insulators, and magnetic semiconductors
Hysteresis and compensation behaviors of spin-3/2 cylindrical Ising nanotube system
International Nuclear Information System (INIS)
Kocakaplan, Yusuf; Keskin, Mustafa
2014-01-01
The hysteresis and compensation behaviors of the spin-3/2 cylindrical Ising nanotube system are studied within the framework of the effective-field theory with correlations. The effects of the Hamiltonian parameters are investigated on the magnetic and thermodynamic quantities, such as the total magnetization, hysteresis curves, and compensation behaviors of the system. Depending on the Hamiltonian parameters, some characteristic hysteresis behaviors are found, such as the existence of double and triple hysteresis loops. According to Néel classification nomenclature, the system displays Q-, R-, P-, N-, M-, and S- types of compensation behaviors for the appropriate values of the system parameters. We also compare our results with some recently published theoretical and experimental works and find a qualitatively good agreement
Hysteresis and compensation behaviors of spin-3/2 cylindrical Ising nanotube system
Energy Technology Data Exchange (ETDEWEB)
Kocakaplan, Yusuf [Graduate School of Natural and Applied Sciences, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2014-09-07
The hysteresis and compensation behaviors of the spin-3/2 cylindrical Ising nanotube system are studied within the framework of the effective-field theory with correlations. The effects of the Hamiltonian parameters are investigated on the magnetic and thermodynamic quantities, such as the total magnetization, hysteresis curves, and compensation behaviors of the system. Depending on the Hamiltonian parameters, some characteristic hysteresis behaviors are found, such as the existence of double and triple hysteresis loops. According to Néel classification nomenclature, the system displays Q-, R-, P-, N-, M-, and S- types of compensation behaviors for the appropriate values of the system parameters. We also compare our results with some recently published theoretical and experimental works and find a qualitatively good agreement.
Self-organization of domain growth in the Ising model with impurities
DEFF Research Database (Denmark)
Andersen, Jørgen Vitting; Mouritsen, Ole G.
1992-01-01
We have studied avalanchelike rearrangements of domain patterns in the two-dimensional Ising model with static impurities, which is quenched to low temperatures. When breaking the up-down symmetry of the spins by a small applied field, the mere fluctuation of a single spin eventually results...... in a cascade of spin flips at the domain boundaries. We have analyzed the lifetime and size distribution functions for the avalanches and related the results to the general phenomena of self-organized criticality and to recent experiments on cellular magnetic domain patterns in magnetic garnet films. Our...... results suggest that the self-organized state in this system appears to be subcritical, in agreement with a recent theory....
Sampling algorithms for validation of supervised learning models for Ising-like systems
Portman, Nataliya; Tamblyn, Isaac
2017-12-01
In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ;ID-MH; that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new ;block-ID; sampling strategy: it decomposes the given structure into square blocks with lattice dimension N ≤ 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).
Precision islands in the Ising and O(N) models
Energy Technology Data Exchange (ETDEWEB)
Kos, Filip [Department of Physics, Yale University, New Haven, CT 06520 (United States); Poland, David [Department of Physics, Yale University, New Haven, CT 06520 (United States); School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States); Simmons-Duffin, David [School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States); Vichi, Alessandro [Theory Division, CERN, Geneva (Switzerland)
2016-08-04
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ{sub σ},Δ{sub ϵ},λ{sub σσϵ},λ{sub ϵϵϵ})=(0.5181489(10),1.412625(10),1.0518537(41),1.532435(19)), give the most precise determinations of these quantities to date.
Precision Islands in the Ising and $O(N)$ Models
Kos, Filip; Simmons-Duffin, David; Vichi, Alessandro
2016-01-01
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, $O(2)$, and $O(3)$ models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, $(\\Delta_{\\sigma}, \\Delta_{\\epsilon},\\lambda_{\\sigma\\sigma\\epsilon}, \\lambda_{\\epsilon\\epsilon\\epsilon}) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19))$, give the most precise determinations of these quantities to date.
Genus-two characters of the Ising model
International Nuclear Information System (INIS)
Choi, J.H.; Koh, I.G.
1989-01-01
As a first step in studying conformal theories on a higher-genus Riemann surface, we construct genus-two characters of the Ising model from their behavior in zero- and nonzero-homology pinching limits, the Goddard-Kent-Oliveco set-space construction, and the branching coefficients in the level-two A 1 /sup (1)/ Kac-Moody characters on the higher-genus Riemann surface
Ising model on tangled chain - 1: Free energy and entropy
International Nuclear Information System (INIS)
Mejdani, R.
1993-04-01
In this paper we have considered an Ising model defined on tangled chain, in which more bonds have been added to those of pure Ising chain. to understand their competition, particularly between ferromagnetic and antiferromagnetic bonds, we have studied, using the transfer matrix method, some simple analytical calculations and an iterative algorithm, the behaviour of the free energy and entropy, particularly in the zero-field and zero temperature limit, for different configurations of the ferromagnetic tangled chain and different types of addition interaction (ferromagnetic or antiferromagnetic). We found that the condition J=J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a ''transition-region'' condition for this behaviour. Our results indicate also the existence of non-zero entropy at zero temperature. (author). 17 refs, 8 figs
Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction
International Nuclear Information System (INIS)
Wang Qiong; He Zhi; Yao Chun-Mei
2015-01-01
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46 (2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated. (paper)
Energy Technology Data Exchange (ETDEWEB)
Keskin, Mustafa, E-mail: keskin@erciyes.edu.t [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Kantar, Ersin [Institute of Science, Erciyes University, 38039 Kayseri (Turkey)
2010-09-15
We study the existence of dynamic compensation temperatures in the mixed spin-1 and spin-3/2 Ising ferrimagnetic system Hamiltonian with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice. We employ the Glauber transitions rates to construct the mean-field dynamic equations. We investigate the time dependence of an average sublattice magnetizations, the thermal behavior of the dynamic sublattice magnetizations and the total magnetization. From these studies, we find the phases in the system, and characterize the nature (continuous or discontinuous) of transitions as well as obtain the dynamic phase transition (DPT) points and the dynamic compensation temperatures. We also present dynamic phase diagrams, including the compensation temperatures, in the five different planes. A comparison is made with the results of the available mixed spin Ising systems.
International Nuclear Information System (INIS)
Keskin, Mustafa; Kantar, Ersin
2010-01-01
We study the existence of dynamic compensation temperatures in the mixed spin-1 and spin-3/2 Ising ferrimagnetic system Hamiltonian with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice. We employ the Glauber transitions rates to construct the mean-field dynamic equations. We investigate the time dependence of an average sublattice magnetizations, the thermal behavior of the dynamic sublattice magnetizations and the total magnetization. From these studies, we find the phases in the system, and characterize the nature (continuous or discontinuous) of transitions as well as obtain the dynamic phase transition (DPT) points and the dynamic compensation temperatures. We also present dynamic phase diagrams, including the compensation temperatures, in the five different planes. A comparison is made with the results of the available mixed spin Ising systems.
The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice
Heydenreich, Markus; Kolesnikov, Leonid
2018-04-01
We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).
Weigel, Martin
2011-09-01
Over the last couple of years it has been realized that the vast computational power of graphics processing units (GPUs) could be harvested for purposes other than the video game industry. This power, which at least nominally exceeds that of current CPUs by large factors, results from the relative simplicity of the GPU architectures as compared to CPUs, combined with a large number of parallel processing units on a single chip. To benefit from this setup for general computing purposes, the problems at hand need to be prepared in a way to profit from the inherent parallelism and hierarchical structure of memory accesses. In this contribution I discuss the performance potential for simulating spin models, such as the Ising model, on GPU as compared to conventional simulations on CPU.
Ising model of financial markets with many assets
Eckrot, A.; Jurczyk, J.; Morgenstern, I.
2016-11-01
Many models of financial markets exist, but most of them simulate single asset markets. We study a multi asset Ising model of a financial market. Each agent has two possible actions (buy/sell) for every asset. The agents dynamically adjust their coupling coefficients according to past market returns and external news. This leads to fat tails and volatility clustering independent of the number of assets. We find that a separation of news into different channels leads to sector structures in the cross correlations, similar to those found in real markets.
Kiely, Thomas G.; Freericks, J. K.
2018-02-01
In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the X Y model in no field (when measurements are performed at the proper stroboscopic times). We describe the details for how this relationship works and, in particular, we also show under what circumstances it fails. We examine wave-function overlap between the two models and observables, such as spin-spin Green's functions. In general, the mapping is quite robust at short times, but will ultimately fail if the run time becomes too long. There is also a tradeoff between the length of time one can run a simulation out to and the time jitter of the stroboscopic measurements that must be balanced when planning to employ this mapping.
Recurrence relations in the three-dimensional Ising model
International Nuclear Information System (INIS)
Yukhnovskij, I.R.; Kozlovskij, M.P.
1977-01-01
Recurrence relations between the coefficients asub(2)sup((i)), asub(4)sup((i)) and Psub(2)sup((i)), Psub(4)sup((i)) which characterize the probabilities of distribution for the three-dimensional Ising model are studied. It is shown that for large arguments z of the Makdonald functions Ksub(ν)(z) the recurrence relations correspond to the known Wilson relations. But near the critical point for small values of the transfer momentum k this limit case does not take place. In the pointed region the argument z tends to zero, and new recurrence relations take place
Ising percolation in a three-state majority vote model
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Martínez-Cruz, M.A.; Gayosso Martínez, Felipe [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-05
Highlights: • Three-state non-consensus majority voter model is introduced. • Phase transition in the absorbing state non-consensus is revealed. • The percolation transition belongs to the universality class of Ising percolation. • The effect of an updating rule for a tie between voter neighbors is highlighted. - Abstract: In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the “magnetization” of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
Ising percolation in a three-state majority vote model
International Nuclear Information System (INIS)
Balankin, Alexander S.; Martínez-Cruz, M.A.; Gayosso Martínez, Felipe; Mena, Baltasar; Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier
2017-01-01
Highlights: • Three-state non-consensus majority voter model is introduced. • Phase transition in the absorbing state non-consensus is revealed. • The percolation transition belongs to the universality class of Ising percolation. • The effect of an updating rule for a tie between voter neighbors is highlighted. - Abstract: In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the “magnetization” of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
The Ising model in the scaling limit as model for the description of elementary particles
International Nuclear Information System (INIS)
Weinzierl, W.
1981-01-01
In this thesis a possible way is stepped over which starts from the derivation of a quantum field theory from simplest statistical degrees of freedom, as for instance in a two-level system. On a model theory, the Ising model in (1+1) dimensions the idea is explained. In this model theory two particle-interpretable quantum fields arise which can be constructed by a basic field which parametrizes the local dynamics in a simplest way. This so called proliferation is further examined. For the proliferation of the basic field a conserved quantity, a kind of parity is necessary. The stability of both particle fields is a consequence of this conservation law. For the identification of the ''particle-interpretable'' fields the propagators of the order and disorder parameter field are calculated and discussed. An effective Hamiltonian in this particle fields is calculated. As further aspect of this transition from the statistical system to quantum field theory the dimensional transmutation and the closely to this connected mass renormalization is examined. The relation between spin systems in the critical region and fermionic field theories is explained. Thereby it results that certain fermionic degrees of freedom of the spin system vanish in the scaling limit. The ''macroscopically'' relevant degrees of freedom constitute a relativistic Majorana field. (orig./HSI) [de
Ising and Potts models: binding disorder-and dimension effects
International Nuclear Information System (INIS)
Curado, E.M.F.
1983-01-01
Within the real space renormalization group framework, some thermal equilibrium properties of pure and disordered insulating systems are calculated. In the pure hypercubic lattice system, the Ising model surface tension and the correlation length of the q-state Potts model, which generalizes the former are analyzed. Several asymptotic behaviors are obtained (for the first time as far as we know) for both functions and the influence of dimension over them can be observed. Accurate numerical proposals for the surface tension are made in several dimensions, and the effect of the number of states (q) on the correlation lenght is shown. In disordered systems, attention is focused essentiall on those which can be theoretically represented by pure sistem Hamiltonians where probability distributions are assumed for the coupling constants (disorder in the bonds). It is obtained with high precision several approximate critical surfaces for the quenched square-lattice Ising model, whose probability distribution can assume two positive values (hence there is no frustration). These aproximate surfaces contain all the exact known points. In the cases where the coupling constant probability distribution can also assume negative values (allowing disordered and frustrated systems), a theoretical treatment which distinguishes the frustration effect from the dilution one is proposed. This distinction can be seen by the different ways in which the bonds of any series-parallel topological array combine. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Deviren, Bayram [Institute of Science, Erciyes University, Kayseri 38039 (Turkey); Canko, Osman [Department of Physics, Erciyes University, Kayseri 38039 (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, Kayseri 38039 (Turkey)], E-mail: keskin@erciyes.edu.tr
2008-09-15
The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.
International Nuclear Information System (INIS)
Deviren, Bayram; Canko, Osman; Keskin, Mustafa
2008-01-01
The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior
International Nuclear Information System (INIS)
Huang, W C; Huo, L; Tian, G; Qian, H R; Gao, X S; Qin, M H; Liu, J-M
2012-01-01
The magnetization behaviors and spin configurations of the classical Ising model on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the fascinating magnetization plateaus observed in TmB 4 and other rare-earth tetraborides. The simulations reproduce the 1/2 magnetization plateau by taking into account the dipole-dipole interaction. In addition, a narrow 2/3 magnetization step at low temperature is predicted in our simulation. The multi-step magnetization can be understood as the consequence of the competitions among the spin-exchange interaction, the dipole-dipole interaction, and the static magnetic energy.
Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling
Sepehrinia, Reza; Chalangari, Fartash
2018-03-01
The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on a distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.
On the quantum symmetry of the chiral Ising model
Vecsernyés, Peter
1994-03-01
We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2012-01-01
The Ising model on a class of infinite random trees is defined as a thermodynamiclimit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application, we study the magnetization properties of such systems and prove that they......The Ising model on a class of infinite random trees is defined as a thermodynamiclimit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application, we study the magnetization properties of such systems and prove...... that they exhibit no spontaneous magnetization. Furthermore, the values of the Hausdorff and spectral dimensions of the underlying trees are calculated and found to be, respectively,¯dh =2 and¯ds = 4/3....
Magnetization plateaus and phase diagrams of the Ising model on the Shastry–Sutherland lattice
Energy Technology Data Exchange (ETDEWEB)
Deviren, Seyma Akkaya, E-mail: sadeviren@nevsehir.edu.tr
2015-11-01
The magnetization properties of a two-dimensional spin-1/2 Ising model on the Shastry–Sutherland lattice are studied within the effective-field theory (EFT) with correlations. The thermal behavior of the magnetizations is investigated in order to characterize the nature (the first- or second-order) of the phase transitions as well as to obtain the phase diagrams of the model. The internal energy, specific heat, entropy and free energy of the system are also examined numerically as a function of the temperature in order to confirm the stability of the phase transitions. The applied field dependence of the magnetizations is also examined to find the existence of the magnetization plateaus. For strong enough magnetic fields, several magnetization plateaus are observed, e.g., at 1/9, 1/8, 1/3 and 1/2 of the saturation. The phase diagrams of the model are constructed in two different planes, namely (h/|J|, |J′|/|J|) and (h/|J|, T/|J|) planes. It was found that the model exhibits first- and second-order phase transitions; hence tricitical point is also observed in additional to the zero-temperature critical point. Moreover the Néel order (N), collinear order (C) and ferromagnetic (F) phases are also found with appropriate values of the system parameters. The reentrant behavior is also obtained whenever model displays two Néel temperatures. These results are compared with some theoretical and experimental works and a good overall agreement has been obtained. - Highlights: • Magnetization properties of spin-1/2 Ising model on SS lattice are investigated. • The magnetization plateaus of the 1/9, 1/8, 1/3 and 1/2 are observed. • The phase diagrams of the model are constructed in two different planes. • The model exhibits the tricitical and zero-temperature critical points. • The reentrant behavior is obtained whenever model displays two Neel temperatures.
Quantum Ising model in transverse and longitudinal fields: chaotic wave functions
International Nuclear Information System (INIS)
Atas, Y Y; Bogomolny, E
2017-01-01
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the Gaussian distribution with zero mean and variance calculated from the first two moments of the Hamiltonian. The main part of the paper is devoted to the discussion of various corrections to the asymptotic result. One type of correction is related to higher order moments of the Hamiltonian, and can be taken into account by Gibbs-like formulae. Other corrections are due to symmetry contributions, which manifest as different numbers of non-zero real and complex coefficients. The statistical model with these corrections included agrees well with numerical calculations of wave function moments. (paper)
High temperature limit of the order parameter correlation functions in the quantum Ising model
Reyes, S. A.; Tsvelik, A. M.
2006-06-01
In this paper we use the exact results for the anisotropic two-dimensional Ising model obtained by Bugrii and Lisovyy [A.I. Bugrii, O.O. Lisovyy, Theor. Math. Phys. 140 (2004) 987] to derive the expressions for dynamical correlation functions for the quantum Ising model in one dimension at high temperatures.
High temperature limit of the order parameter correlation functions in the quantum Ising model
Energy Technology Data Exchange (ETDEWEB)
Reyes, S.A. [Department of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, NY 11794-3840 (United States); Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States); Tsvelik, A.M. [Department of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, NY 11794-3840 (United States) and Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)]. E-mail tsvelik@bnl.gov
2006-06-12
In this paper we use the exact results for the anisotropic two-dimensional Ising model obtained by Bugrii and Lisovyy [A.I. Bugrii, O.O. Lisovyy, Theor. Math. Phys. 140 (2004) 987] to derive the expressions for dynamical correlation functions for the quantum Ising model in one dimension at high temperatures.
Completeness of classical spin models and universal quantum computation
International Nuclear Information System (INIS)
De las Cuevas, Gemma; Dür, Wolfgang; Briegel, Hans J; Van den Nest, Maarten
2009-01-01
We study mappings between different classical spin systems that leave the partition function invariant. As recently shown in Van den Nest et al (2008 Phys. Rev. Lett. 100 110501), the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be 'complete'. However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real—and, hence, 'physical'—couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow for universal quantum computation via local measurements only, and complete classical spin systems
International Nuclear Information System (INIS)
Bahr, Benjamin; Hellmann, Frank; Kaminski, Wojciech; Kisielowski, Marcin; Lewandowski, Jerzy
2011-01-01
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as our main tool. A set of moves we define in the set of the operator spin foams (among other operations) allows us to split the faces and the edges of the foams. We assign to each operator spin foam a contracted operator, by using the contractions at the vertices and suitably adjusted face amplitudes. The emergence of the face amplitudes is the consequence of assuming the invariance of the contracted operator with respect to the moves. Next, we define spin foam models and consider the class of models assumed to be symmetric with respect to the moves we have introduced, and assuming their partition functions (state sums) are defined by the contracted operators. Briefly speaking, those operator spin foam models are invariant with respect to the cellular decomposition, and are sensitive only to the topology and colouring of the foam. Imposing an extra symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with assumed invariance with respect to the edge splitting move, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on a spin(4) BF spin foam model is exactly the way we tend to view 4D quantum gravity, starting with the BC model and continuing with the Engle-Pereira-Rovelli-Livine (EPRL) or Freidel-Krasnov (FK) models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. Among our natural spin foam models there are the BF spin foam model, the BC model, and a model corresponding to the EPRL intertwiners. Our operator spin foam framework can also be used for more general spin
String effects in the 3d gauge Ising model
International Nuclear Information System (INIS)
Caselle, Michele; Panero, Marco; Hasenbusch, Martin
2003-01-01
We compare the predictions of the effective string description of confinement with a set of Monte Carlo data for the 3d gauge Ising model at finite temperature. Thanks to a new algorithm which makes use of the dual symmetry of the model we can reach very high precisions even for large quark-antiquark distances. We are thus able to explore the large R regime of the effective string. We find that for large enough distances and low enough temperature the data are well described by a pure bosonic string. As the temperature increases higher order corrections become important and cannot be neglected even at large distances. These higher order corrections seem to be well described by the Nambu-Goto action truncated at the first perturbative order. (author)
History of the Lenz–Ising model 1965–1971
DEFF Research Database (Denmark)
Niss, Martin
2011-01-01
when it was realized that the Lenz–Ising model is actually relevant for the understanding of phase transitions. In this article, which is self-contained, I study how this realization affected attempts to understand critical phenomena, which can be understood as limiting cases of (first-order) phase...... of critical phenomena, for example that diverse physical systems exhibit similar behavior close to a critical point. Later, a more systematic program of understanding critical phenomena emerged that involved an explicit formulation of what it means to understand critical phenomena, namely, the elucidation...... of what features of the Hamiltonian of models lead to what kinds of behavior close to critical points. Attempts to accomplish this program culminated with the so-called hypothesis of universality, put forward independently by Robert B. Griffiths and Leo P. Kadanoff in 1970. They divided critical phenomena...
Antiferromagnetic Ising model with transverse and longitudinal field
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Kischinhevsky, M.
1985-01-01
We study the quantum hamiltonian version of the Ising Model in one spacial dimension under an external longitudinal (uniform) field at zero temperature. A phenomenological renormalization group procedure is used to obtain the phase diagram; the transverse and longitudinal zero field limits are studied and we verify the validity of universality at non zero transverse fields, where two-dimensional critical behaviour is obtained. To perform the numerical calculations we use the Lanczos scheme, which gives highly precise results with rather short processing times. We also analyse the possibility of using these techniques to extend the present work to the quantum hamiltonian version of the q-state Potts Model (q>2) in larger system. (author) [pt
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
Salathé, Y.; Mondal, M.; Oppliger, M.; Heinsoo, J.; Kurpiers, P.; Potočnik, A.; Mezzacapo, Antonio; Las Heras García, Urtzi; Lamata Manuel, Lucas; Solano Villanueva, Enrique Leónidas; Filipp, S.; Wallraff, A.
2015-01-01
Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit...
Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field
Borelli, M. E. S.; Carneiro, C. E. I.
1996-02-01
We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P( Δi) = pδ( Δi - Δ) + (1 - p) δ( Δi). We analyse the effects of randomness on the first-order surfaces of the Δ- T- H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.
Effective-field theory on the kinetic Ising model
International Nuclear Information System (INIS)
Shi Xiaoling; Wei Guozhu; Li Lin
2008-01-01
As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT)
de Albuquerque, Douglas F.; Fittipaldi, I. P.
1994-05-01
A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.
Shi, Kaile; Jiang, Wei; Guo, Anbang; Wang, Kai; Wu, Chuang
2018-06-01
The magnetic and thermodynamic properties of borophene structure have been studied for the first time by Monte Carlo simulation. Two-dimensional borophene structure consisting of seven hexagonal B36 units is described by Ising model. Each B36 basic unit includes three benzene-like with spin-3/2. The general formula for the borophene structure is given. The numerical results of the magnetization, the magnetic susceptibility, the internal energy and the specific heat are studied with various parameters. The possibility to test the predicted magnetism in experiment are illustrated, for instance, the maximum on the magnetization curve. The multiple hysteresis loops and the magnetization plateaus are sensitive to the ferromagnetic or ferrimagnetic exchange coupling in borophene structure. The results show the borophene structure could have applications in spintronics, which deserves further studies in experiments.
Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model
O'Brien, Edward; Fendley, Paul
2018-05-01
We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.
Quantum decoration transformation for spin models
Energy Technology Data Exchange (ETDEWEB)
Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre, E-mail: ors@dfi.ufla.br
2016-09-15
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.
Quantum decoration transformation for spin models
International Nuclear Information System (INIS)
Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre
2016-01-01
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.
Generation of Control by SU(2) Reduction for the Anisotropic Ising Model
International Nuclear Information System (INIS)
Delgado, F
2016-01-01
Control of entanglement is fundamental in Quantum Information and Quantum Computation towards scalable spin-based quantum devices. For magnetic systems, Ising interaction with driven magnetic fields modifies entanglement properties of matter based quantum systems. This work presents a procedure for dynamics reduction on SU(2) subsystems using a non-local description. Some applications for Quantum Information are discussed. (paper)
Study of ±J Ising spin glasses via multicanonical ensemble
International Nuclear Information System (INIS)
Celik, T.; Berg, B.
1993-03-01
The authors performed numerical simulations of 2D and 3D Edwards-Anderson spin glass models by using the recently developed multicanonical ensemble. The ergodicity times increase with the lattice size approximately as V 3 . The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored
International Nuclear Information System (INIS)
Nishiyama, Yoshihiro
2011-01-01
A length-N spin chain with the √N(=v)th neighbor interaction is identical to a two-dimensional (d = 2) model under the screw-boundary (SB) condition. The SB condition provides a flexible scheme to construct a d ≥ 2 cluster from an arbitrary number of spins; the numerical diagonalization combined with the SB condition admits a potential applicability to a class of systems intractable with the quantum Monte Carlo method due to the negative-sign problem. However, the simulation results suffer from characteristic finite-size corrections inherent in SB. In order to suppress these corrections, we adjust the screw pitch v(N) so as to minimize the excitation gap for each N. This idea is adapted to the transverse-field Ising model on the triangular lattice with N ≤ 32 spins. As a demonstration, the correlation-length critical exponent ν is analyzed in some detail
Testing Lorentz Invariance Emergence in the Ising Model using Monte Carlo simulations
Dias Astros, Maria Isabel
2017-01-01
In the context of the Lorentz invariance as an emergent phenomenon at low energy scales to study quantum gravity a system composed by two 3D interacting Ising models (one with an anisotropy in one direction) was proposed. Two Monte Carlo simulations were run: one for the 2D Ising model and one for the target model. In both cases the observables (energy, magnetization, heat capacity and magnetic susceptibility) were computed for different lattice sizes and a Binder cumulant introduced in order to estimate the critical temperature of the systems. Moreover, the correlation function was calculated for the 2D Ising model.
Čenčariková, Hana; Strečka, Jozef; Gendiar, Andrej; Tomašovičová, Natália
2018-05-01
An exhaustive ground-state analysis of extended two-dimensional (2D) correlated spin-electron model consisting of the Ising spins localized on nodal lattice sites and mobile electrons delocalized over pairs of decorating sites is performed within the framework of rigorous analytical calculations. The investigated model, defined on an arbitrary 2D doubly decorated lattice, takes into account the kinetic energy of mobile electrons, the nearest-neighbor Ising coupling between the localized spins and mobile electrons, the further-neighbor Ising coupling between the localized spins and the Zeeman energy. The ground-state phase diagrams are examined for a wide range of model parameters for both ferromagnetic as well as antiferromagnetic interaction between the nodal Ising spins and non-zero value of external magnetic field. It is found that non-zero values of further-neighbor interaction leads to a formation of new quantum states as a consequence of competition between all considered interaction terms. Moreover, the new quantum states are accompanied with different magnetic features and thus, several kinds of field-driven phase transitions are observed.
Comment on "Many-body localization in Ising models with random long-range interactions"
Maksymov, Andrii O.; Rahman, Noah; Kapit, Eliot; Burin, Alexander L.
2017-11-01
This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r-α, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015), 10.1103/PhysRevB.91.094202] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for α ≤2 d in a d -dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 ≤α ≤d . The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)type="doi" specific-use="suppress-display">10.1103/PhysRevA.94.063625].
Ising formulations of many NP problems
Lucas, Andrew
2013-01-01
We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.
Ising formulations of many NP problems
Directory of Open Access Journals (Sweden)
Andrew eLucas
2014-02-01
Full Text Available We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.
Ising percolation in a three-state majority vote model
Balankin, Alexander S.; Martínez-Cruz, M. A.; Gayosso Martínez, Felipe; Mena, Baltasar; Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier
2017-02-01
In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the "magnetization" of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
Ferrimagnetism and compensation points in a decorated 3D Ising model
International Nuclear Information System (INIS)
Oitmaa, J.; Zheng, W.
2003-01-01
Full text: Ferrimagnets are materials where ions on different sublattices have opposing magnetic moments which do not exactly cancel even at zero temperature. An intriguing possibility then is the existence of a compensation point, below the Curie temperature, where the net moment changes sign. This has obvious technological significance. Most theoretical studies of such systems have used mean-field approaches, making it difficult to distinguish real properties of the model from artefacts of the approximation. For this reason a number of simpler models have been proposed, where treatments beyond mean-field theory are possible. Of particular interest are decorated systems, which can be mapped exactly onto simpler models and, in this way, either solved exactly or to a high degree of numerical precision. We use this approach to study a ferrimagnetic Ising system with spins 1/2 at the sites of a simple cubic lattice and spins S=1 or 3/2 located on the bonds. Our results, which are exact to high numerical precision, show a number of surprising and interesting features: for S=1 the possibility of zero, one or two compensation points, re-entrant behaviour, and up to three critical points; for S=3/2 always a simple critical point and zero or one compensation point
Excited TBA equations I: Massive tricritical Ising model
International Nuclear Information System (INIS)
Pearce, Paul A.; Chim, Leung; Ahn, Changrim
2001-01-01
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II
International Nuclear Information System (INIS)
Keskin, M.; Canko, O.; Gueldal, S.
2009-01-01
We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.
Energy Technology Data Exchange (ETDEWEB)
Keskin, M., E-mail: keskin@erciyes.edu.t [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Canko, O. [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Gueldal, S. [Institute of Science, Erciyes University, 38039 Kayseri (Turkey)
2009-12-14
We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.
International Nuclear Information System (INIS)
Jullien, R.; Pfeuty, P.; Fields, J.N.; Doniach, S.
1978-01-01
A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical ''magnetic'' exponents near the transition
Ising model of a randomly triangulated random surface as a definition of fermionic string theory
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Bershadsky, M.A.; Migdal, A.A.
1986-01-01
Fermionic degrees of freedom are added to randomly triangulated planar random surfaces. It is shown that the Ising model on a fixed graph is equivalent to a certain Majorana fermion theory on the dual graph. (orig.)
Gálisová, Lucia
2018-05-01
Ground-state properties of a hybrid double-tetrahedral chain, in which the localized Ising spins regularly alternate with triangular plaquettes occupied by a variable number of mobile electrons, are exactly investigated. We demonstrate that the zero-temperature phase diagram of the model involves several non-degenerate, two-fold degenerate and macroscopically degenerate chiral phases. Low-temperature dependencies of the entropy and specific heat are also examined in order to gain a deeper insight into the degeneracy of individual ground-state phases and phase transitions. It is shown that a diversity of the ground-state degeneracy manifests itself in multiple-peak structures of both thermodynamic quantities. A remarkable temperature dependencies of the specific heat with two and three Schottky-type maxima are discussed in detail.
A coherent Ising machine for 2000-node optimization problems
Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki
2016-11-01
The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
Nonequilibrium two-dimensional Ising model with stationary uphill diffusion
Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia
2018-03-01
Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.
Aging, rejuvenation, and memory effects in short-range Ising spin glass: Cu_0.5Co_0.5Cl_2-FeCl3 GBIC
Suzuki, M.; Suzuki, I. S.
2004-03-01
Cu_0.5Co_0.5Cl_2-FeCl3 GBIC undergoes a spin glass (SG) transition at Tg (= 3.92 ± 0.11 K). The system shows a dynamic behavior that has some similarities and some significant differences compared to a 3D Ising SG.^1 Here we report on non-equilibrium aging dynamics which has been studied using zero-field cooled (ZFC) magnetization and low frequency AC magnetic susceptibility.^2 The time dependence of the relaxation rate S(t) = (1/H)dM_ZFC/dln t for the ZFC magnetization after the ZFC aging protocol, shows a peak at a characteristic time t_cr near a wait time t_w, corresponding to a crossover from quasi equilibrium dynamics to non-equilibrium. The time t_cr strongly depends on t_w, temperature, magnetic field, and the temperature shift. The rejuvenation effect is observed in both i^' and i^'' under the T-shift and H-shift procedures. The memory of the specific spin configurations imprinted during the ZFC aging protocol can be recalled when the system is re-heated at a constant heating rate. The aging, rejuvenation, and memory effects are discussed in terms of the scaling concepts derived from numerical studies on 3D Edwards-Anderson spin glass model. 1. I.S. Suzuki and M. Suzuki, Phys. Rev. B 68, 094424 (2003) 2. M. Suzuki and I.S. Suzuki, cond-mat/0308285
Linking market interaction intensity of 3D Ising type financial model with market volatility
Fang, Wen; Ke, Jinchuan; Wang, Jun; Feng, Ling
2016-11-01
Microscopic interaction models in physics have been used to investigate the complex phenomena of economic systems. The simple interactions involved can lead to complex behaviors and help the understanding of mechanisms in the financial market at a systemic level. This article aims to develop a financial time series model through 3D (three-dimensional) Ising dynamic system which is widely used as an interacting spins model to explain the ferromagnetism in physics. Through Monte Carlo simulations of the financial model and numerical analysis for both the simulation return time series and historical return data of Hushen 300 (HS300) index in Chinese stock market, we show that despite its simplicity, this model displays stylized facts similar to that seen in real financial market. We demonstrate a possible underlying link between volatility fluctuations of real stock market and the change in interaction strengths of market participants in the financial model. In particular, our stochastic interaction strength in our model demonstrates that the real market may be consistently operating near the critical point of the system.
Stramaglia, S.; Pellicoro, M.; Angelini, L.; Amico, E.; Aerts, H.; Cortés, J. M.; Laureys, S.; Marinazzo, D.
2017-04-01
Dynamical models implemented on the large scale architecture of the human brain may shed light on how a function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the critical state), the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between the structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of a homeostatic principle imposed to neural activity.
Restoration of dimensional reduction in the random-field Ising model at five dimensions
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2017-04-01
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D equality at all studied dimensions.
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
Mo, Qianxing; Liang, Faming
2010-01-01
approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic
International Nuclear Information System (INIS)
Deviren, Bayram; Polat, Yasin; Keskin, Mustafa
2011-01-01
The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point (TP), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Néel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions. (general)
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Temizer, Ümüt
2014-01-01
In this study, the dynamic critical behavior of the mixed spin-1 and spin-3/2 Ising system on a bilayer square lattice is studied by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic (FM/FM) and antiferromagnetic/ferromagnetic (AFM/FM) interactions in the presence of a time-varying external magnetic field. The dynamic equations describing the time-dependencies of the average magnetizations are derived from the Master equation. The phases in the system are obtained by solving these dynamic equations. The temperature dependence of the dynamic magnetizations is investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions and to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are constructed in seven different planes for both FM/FM and AFM/FM interactions and the effects of the related interaction parameters on the dynamic phase diagrams are examined. It is found that the dynamic phase diagrams display many dynamic critical points, such as tricritical point, triple point (TP), quadruple point (QP), double critical end point (B), multicritical point (A) and tetracritical point (M). Moreover, the reentrant behavior is observed for AFM/FM interaction in the system. - Highlights: • The mixed spin (1, 3/2) Ising system is studied on a two-layer square lattice. • The Glauber transition rates are employed to construct the dynamic equations. • The dynamic phase diagrams are presented in seven different planes. • The system displays many dynamic critical points. • The reentrant behavior is observed for AFM/FM interaction
Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
Steinhaus, Sebastian
2015-09-01
The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretization. However, extracting these mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories. Therefore, we introduce a simple two-dimensional toy model for Yang-Mills coupled to spin foams, namely an Ising model coupled to so-called intertwiner models defined for SU (2 )k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretization. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.
Singh, R. R. P.; Young, A. P.
2017-08-01
We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.
Evaluation of tranche in securitization and long-range Ising model
Kitsukawa, K.; Mori, S.; Hisakado, M.
2006-08-01
This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J/N and the external field H as a model for homogeneous credit portfolio of assets with default probability Pd and default correlation ρd. Based on the discussion on the (J,H) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for Pd,ρd and the normalization factor Z in terms of the model parameters N and J,H. The effect of the default correlation ρd on the probabilities P(Nd,ρd) for Nd defaults and on the cumulative distribution function D(i,ρd) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρd and that of the senior tranche increases linearly, which are important in their pricing and ratings.
Probabilistic image processing by means of the Bethe approximation for the Q-Ising model
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Tanaka, Kazuyuki; Inoue, Jun-ichi; Titterington, D M
2003-01-01
The framework of Bayesian image restoration for multi-valued images by means of the Q-Ising model with nearest-neighbour interactions is presented. Hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We conclude that, in real world grey-level images, the Q-Ising model can give us good results
Phase transitions in the random field Ising model in the presence of a transverse field
Energy Technology Data Exchange (ETDEWEB)
Dutta, A.; Chakrabarti, B.K. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India); Stinchcombe, R.B. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India); Department of Physics, Oxford (United Kingdom)
1996-09-07
We have studied the phase transition behaviour of the random field Ising model in the presence of a transverse (or tunnelling) field. The mean field phase diagram has been studied in detail, and in particular the nature of the transition induced by the tunnelling (transverse) field at zero temperature. Modified hyper-scaling relation for the zero-temperature transition has been derived using the Suzuki-Trotter formalism and a modified 'Harris criterion'. Mapping of the model to a randomly diluted antiferromagnetic Ising model in uniform longitudinal and transverse field is also given. (author)
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Approximate critical surface of the bond-mixed square-lattice Ising model
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Levy, S.V.F.; Tsallis, C.; Curado, E.M.F.
1979-09-01
The critical surface of the quenched bond-mixed square-lattice spin-1/2 first-neighbour-interaction ferromagnetic Ising model (with exchange interactions J 1 and J 2 ) has been investigated. Through renormalization group and heuristical procedures, a very accurate (error inferior to 3x10 -4 in the variables t sub(i) = th (J sub(i)/k sub(b)T)) approximate numerical proposal for all points of this surface is presented. This proposal simultaneously satisfies all the available exact results concerning the surface, namely P sub(c) = 1/2, t sub(c) = √2 - 1, both limiting slopes in these points, and t 2 = (1-t 1 )/(1+t 1 ) for p = 1/2. Furthemore an analytic approximation (namely (1 - p) 1n(1 + t 1 ) + p 1n(1 + t 2 ) =(1/2)1n 2) is also proposed. In what concerns the available exact results, it only fails in reproducing one of the two limiting slopes, where there is an error of 1% in the derivative: these facts result in an estimated error less than 10 -3 (in the t-variables) for any points in the surface. (Author) [pt
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-01-01
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435
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Masrour, R.; Jabar, A.; Benyoussef, A.; Hamedoun, M.
2016-01-01
In this work, we have studied and compared the magnetic properties of Ising spins-5/2 and 3/2 systems on decorated square and triangular lattices using the Monte Carlo simulations. The transition temperature of the two-dimensional decorated square and triangular lattices has been obtained. The effect of the exchange interactions and crystal field on the magnetization is investigated. The magnetic coercive field and saturation magnetization of the two-dimensional decorated square and triangular lattices have been obtained.
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); Jabar, A. [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); Benyoussef, A. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2016-07-15
In this work, we have studied and compared the magnetic properties of Ising spins-5/2 and 3/2 systems on decorated square and triangular lattices using the Monte Carlo simulations. The transition temperature of the two-dimensional decorated square and triangular lattices has been obtained. The effect of the exchange interactions and crystal field on the magnetization is investigated. The magnetic coercive field and saturation magnetization of the two-dimensional decorated square and triangular lattices have been obtained.
Long-range transverse Ising model built with dipolar condensates in two-well arrays
International Nuclear Information System (INIS)
Li, Yongyao; Pang, Wei; Xu, Jun; Lee, Chaohong; Malomed, Boris A; Santos, Luis
2017-01-01
Dipolar Bose–Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic–antiferromagnetic phase transition, and non-trivial phases due to frustration. The considered setup allows as well for the study of Kibble–Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field one-dimensional transverse Ising model. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and local transverse fields, that may lead to the Anderson-like localization of imbalance perturbations. (paper)
Monte Carlo Simulations of Compressible Ising Models: Do We Understand Them?
Landau, D. P.; Dünweg, B.; Laradji, M.; Tavazza, F.; Adler, J.; Cannavaccioulo, L.; Zhu, X.
Extensive Monte Carlo simulations have begun to shed light on our understanding of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg-Wilson hamiltonian for systems with elastic degrees of freedom resulted in the prediction that there should be four distinct cases that would have different behavior, depending upon symmetries and thermodynamic constraints. We shall provide an account of the results of careful Monte Carlo simulations for a simple compressible Ising model that can be suitably modified so as to replicate all four cases.
Canonical vs. micro-canonical sampling methods in a 2D Ising model
International Nuclear Information System (INIS)
Kepner, J.
1990-12-01
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.
Physics and financial economics (1776–2014): puzzles, Ising and agent-based models
International Nuclear Information System (INIS)
Sornette, Didier
2014-01-01
This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets. (key issues reviews)
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics--from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
Directory of Open Access Journals (Sweden)
Y. Salathé
2015-06-01
Full Text Available Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.
Ising critical behaviour in the one-dimensional frustrated quantum XY model
International Nuclear Information System (INIS)
Granato, E.
1993-06-01
A generalization of the one-dimensional frustrated quantum XY model is considered in which the inter and intra-chain coupling constants of the two infinite XY (planar rotor) chains have different strengths. The model can describe the superconductor-insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical XY-Ising model. The critical behaviour is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal inter and intra-chain coupling constants, the XY and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behaviour for the chirality order parameter in good agreement with the results for the XY-Ising model. (author). 18 refs, 4 figs
Energy Technology Data Exchange (ETDEWEB)
Deviren, Şeyma Akkaya, E-mail: sadeviren@nevsehir.edu.tr [Department of Science Education, Education Faculty, Nevsehir Hacı Bektaş Veli University, 50300 Nevşehir (Turkey); Deviren, Bayram [Department of Physics, Nevsehir Hacı Bektaş Veli University, 50300 Nevsehir (Turkey)
2016-03-15
The dynamic phase transitions and dynamic phase diagrams are studied, within a mean-field approach, in the kinetic Ising model on the Shastry-Sutherland lattice under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The time-dependence behavior of order parameters and the behavior of average order parameters in a period, which is also called the dynamic order parameters, as a function of temperature, are investigated. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions as well as to obtain the dynamic phase transition temperatures. We present the dynamic phase diagrams in the magnetic field amplitude and temperature plane. The phase diagrams exhibit a dynamic tricritical point and reentrant phenomena. The phase diagrams also contain paramagnetic (P), Néel (N), Collinear (C) phases, two coexistence or mixed regions, (N+C) and (N+P), which strongly depend on interaction parameters. - Highlights: • Dynamic magnetization properties of spin-1/2 Ising model on SSL are investigated. • Dynamic magnetization, hysteresis loop area, and correlation have been calculated. • The dynamic phase diagrams are constructed in (T/|J|, h/|J|) plane. • The phase diagrams exhibit a dynamic tricritical point and reentrant phenomena.
International Nuclear Information System (INIS)
Ohwada, Kenji; Fujii, Yasuhiko; Shobu, Takahisa; Muraoka, Jiro
2008-01-01
Devil's flower has been found in a temperature-pressure phase diagram of NaV 2 O 5 , which shows a charge disproportionation (CD) at ambient pressure. By a complementary use of an x-ray structural analysis and a resonant x-ray diffraction, which is sensitive to CD, we have investigated the structural relationship between two ground states appeared in lower and higher pressure regions including the charge arrangements. It has been clarified that two equivalent types of charge arrangement in CD correspond to the Ising variable in NaV 2 O 5 . The atomic shifts are regarded as linearly coupled to the Ising spins. The results lead us to the conclusion that the devil's flower blooms in a charge-disproportionation system. The results also lead us to a hypothesis that the competitive interactions between Ising spins may result from the Ising spin-phonon coupling. (author)
On the equivalence of Ising models on ‘small-world’ networks and LDPC codes on channels with memory
International Nuclear Information System (INIS)
Neri, Izaak; Skantzos, Nikos S
2014-01-01
We demonstrate the equivalence between thermodynamic observables of Ising spin-glass models on small-world lattices and the decoding properties of error-correcting low-density parity-check codes on channels with memory. In particular, the self-consistent equations for the effective field distributions in the spin-glass model within the replica symmetric ansatz are equivalent to the density evolution equations forr Gilbert–Elliott channels. This relationship allows us to present a belief-propagation decoding algorithm for finite-state Markov channels and to compute its performance at infinite block lengths from the density evolution equations. We show that loss of reliable communication corresponds to a first order phase transition from a ferromagnetic phase to a paramagnetic phase in the spin glass model. The critical noise levels derived for Gilbert–Elliott channels are in very good agreement with existing results in coding theory. Furthermore, we use our analysis to derive critical noise levels for channels with both memory and asymmetry in the noise. The resulting phase diagram shows that the combination of asymmetry and memory in the channel allows for high critical noise levels: in particular, we show that successful decoding is possible at any noise level of the bad channel when the good channel is good enough. Theoretical results at infinite block lengths using density evolution equations aree compared with average error probabilities calculated from a practical implementation of the corresponding decoding algorithms at finite block lengths. (paper)
Zero-temperature renormalization of the 2D transverse Ising model
International Nuclear Information System (INIS)
Kamieniarz, G.
1982-08-01
A zero-temperature real-space renormalization-group method is applied to the transverse Ising model on planar hexagonal, triangular and quadratic lattices. The critical fields and the critical exponents describing low-field large-field transition are calculated. (author)
Annealed central limit theorems for the ising model on random graphs
Giardinà, C.; Giberti, C.; van der Hofstad, R.W.; Prioriello, M.L.
2016-01-01
The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by √N of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random graph (or generalized random graph), the 2-regular configuration
Finite cluster renormalization and new two step renormalization group for Ising model
International Nuclear Information System (INIS)
Benyoussef, A.; El Kenz, A.
1989-09-01
New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs
First steps towards a state classification in the random-field Ising model
International Nuclear Information System (INIS)
Basso, Vittorio; Magni, Alessandro; Bertotti, Giorgio
2006-01-01
The properties of locally stable states of the random-field Ising model are studied. A map is defined for the dynamics driven by the field starting from a locally stable state. The fixed points of the map are connected with the limit hysteresis loops that appear in the classification of the states
Monte Carlo simulation of Ising models by multispin coding on a vector computer
Wansleben, Stephan; Zabolitzky, John G.; Kalle, Claus
1984-11-01
Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.
Exact solution of an Ising model with competing interactions on a Cayley tree
Ganikhodjaev, N N; Wahiddin, M R B
2003-01-01
The exact solution of an Ising model with competing restricted interactions on the Cayley tree, and in the absence of an external field is presented. A critical curve is defined where it is possible to get phase transitions above it, and a single Gibbs state is obtained elsewhere.
Dynamic of Ising model with transverse field for two coupled sublattices in disordered phase
International Nuclear Information System (INIS)
Sa Motta, C.E.H. de.
1984-02-01
The dynamics of the two coupled sublattices tridimensional Ising model in a transverse field was studied by means of a continued fraction expansion for coupled operators. The static Correlation Functions necessary for studying the dynamics were calculated with the Green's Functions Method in the Random Phase Approximation (RPA). The spectral function was calculated in the region T c → . (Author) [pt
Study on non-universal critical behaviour in Ising model with defects
International Nuclear Information System (INIS)
Guimaraes, L.G.
1986-01-01
One-dimensional quantum analogous of two-dimensional Ising models with line and step type linear defects are studied. The phenomenological renormalization group was approached using conformal invariance for relating critical exponent N sup(*) sub(H). Aiming to obtain the Hamiltonian diagonal, Lanczos tridiagonal method was used. (H.C.K.)
Magnetic properties of the three-dimensional Ising model with an interface amorphization
International Nuclear Information System (INIS)
Benyoussef, A.; El Kenz, A.; Saber, M.
1993-09-01
A three-dimensional ferromagnetic Ising model with an interface amorphization is investigated with the use of the effective field theory. Phase diagrams and reduced magnetization curves of interface and bulks are studied. We obtain a number of characteristic behaviour such as the possibility of the reentrant phenomena and a large depression of interface magnetization. (author). 21 refs, 5 figs
Modeling of the financial market using the two-dimensional anisotropic Ising model
Lima, L. S.
2017-09-01
We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.
Rotational Invariance of the 2d Spin - Spin Correlation Function
Pinson, Haru
2012-09-01
At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3-5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22-26, 1984, JINR, vol II, pp 138-151, 1985).
Thermodynamics of spin chains of Haldane–Shastry type and one-dimensional vertex models
International Nuclear Information System (INIS)
Enciso, Alberto; Finkel, Federico; González-López, Artemio
2012-01-01
We study the thermodynamic properties of spin chains of Haldane–Shastry type associated with the A N−1 root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains’ thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane–Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models. - Highlights: ► Partition function of spin chains of Haldane–Shastry type in magnetic field. ► Equivalence to classical inhomogeneous Ising models. ► Free energy per site, other thermodynamic quantities in thermodynamic limit. ► Zero field, zero temperature limits. ► Thermodynamic equivalence with ensemble of classical Ising models.
International Nuclear Information System (INIS)
Martin, H.O.; Tsallis, C.
1981-01-01
A simple renormalization group approach based on self-dual clusters is proposed for two-dimensional nearest-neighbour 1/2 - spin Ising model on the square lattice; it reproduces the exact critical point. The internal energy and the specific heat for vanishing external magnetic field, spontaneous magnetization and the thermal (Y sub(T)) and magnetic (Y sub(H)) critical exponents are calculated. The results obtained from the first four smallest cluster sizes strongly suggest the convergence towards the exact values when the cluster sizes increases. Even for the smallest cluster, where the calculation is very simple, the results are quite accurate, particularly in the neighbourhood of the critical point. (Author) [pt
Monte Carlo simulations of the Spin-2 Blume-Emery-Griffiths model
International Nuclear Information System (INIS)
Iwashita, Takashi; Uragami, Kakuko; Muraoka, Yoshinori; Kinoshita, Takehiro; Idogaki, Toshihiro
2010-01-01
The magnetic properties of the spin S = 2 Ising system with the bilinear exchange interaction J 1 S iz S jz , the biquadratic exchange interaction J 2 S iz 2 S jz 2 and the single-ion anisotropy DS iz 2 are discussed by making use of the Monte Carlo (MC) simulation for the magnetization z >, sub-lattice magnetizations z (A)> and z (B)>, the magnetic specific heat C M and spin structures. This Ising spin system of S = 2 with interactions J 1 and J 2 and with anisotropy D corresponds to the spin-2 Blume-Emery-Griffiths model. The phase diagram of this Ising spin system on a two-dimensional square lattice has been obtained for exchange parameter J 2 /J 1 and anisotropy parameter D/J 1 . The shapes of the temperature dependence of sublattice magnetizations z (A)> and z (B)> are related with abnormal behavior of temperature dependence of z > at low temperatures and affected significantly by the single-ion anisotropy D. The staggered quadrupolar (SQ) ordering turns out to be different largely between Ising systems with the single-ion anisotropy (D ≠ 0) and without the one (D 0).
3D-Ising model as a string theory in three-dimensional euclidean space
International Nuclear Information System (INIS)
Sedrakyan, A.
1992-11-01
A three-dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices, which depend on two integers (m,n) are calculated analytically. The critical indices of the three-dimensional Ising model should belong to this set. A possible connection with the chain of three dimensional lattice Pott's models is pointed out. (author) 22 refs.; 2 figs
On Ising - Onsager problem in external magnetic field
International Nuclear Information System (INIS)
Kochmanski, M.S.
1997-01-01
In this paper a new approach to solving the Ising - Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the two dimensional and three dimensional Ising model with interaction of the nearest neighbors are derived. The representations of free energy being expressed by multidimensional integrals of Gauss type with the appropriate dimensionality are shown. Possibility of calculating the integrals and the critical indices on the base of the derived representations for free energy is investigated
Züleyha, Artuç; Ziya, Merdan; Selçuk, Yeşiltaş; Kemal, Öztürk M.; Mesut, Tez
2017-11-01
Computational models for tumors have difficulties due to complexity of tumor nature and capacities of computational tools, however, these models provide visions to understand interactions between tumor and its micro environment. Moreover computational models have potential to develop strategies for individualized treatments for cancer. To observe a solid brain tumor, glioblastoma multiforme (GBM), we present a two dimensional Ising Model applied on Creutz cellular automaton (CCA). The aim of this study is to analyze avascular spherical solid tumor growth, considering transitions between non tumor cells and cancer cells are like phase transitions in physical system. Ising model on CCA algorithm provides a deterministic approach with discrete time steps and local interactions in position space to view tumor growth as a function of time. Our simulation results are given for fixed tumor radius and they are compatible with theoretical and clinic data.
An analysis of intergroup rivalry using Ising model and reinforcement learning
Zhao, Feng-Fei; Qin, Zheng; Shao, Zhuo
2014-01-01
Modeling of intergroup rivalry can help us better understand economic competitions, political elections and other similar activities. The result of intergroup rivalry depends on the co-evolution of individual behavior within one group and the impact from the rival group. In this paper, we model the rivalry behavior using Ising model. Different from other simulation studies using Ising model, the evolution rules of each individual in our model are not static, but have the ability to learn from historical experience using reinforcement learning technique, which makes the simulation more close to real human behavior. We studied the phase transition in intergroup rivalry and focused on the impact of the degree of social freedom, the personality of group members and the social experience of individuals. The results of computer simulation show that a society with a low degree of social freedom and highly educated, experienced individuals is more likely to be one-sided in intergroup rivalry.
Critical Behavior of the Annealed Ising Model on Random Regular Graphs
Can, Van Hao
2017-11-01
In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121-161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by n^{3/4} converges to a specific random variable, with n the number of vertices of random regular graphs.
Single-file water as a one-dimensional Ising model
Energy Technology Data Exchange (ETDEWEB)
Koefinger, Juergen [Laboratory of Chemical Physics, Bldg 5, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892 (United States); Dellago, Christoph, E-mail: koefingerj@mail.nih.go [Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna (Austria)
2010-09-15
We show that single-file water in nanopores can be viewed as a one-dimensional (1D) Ising model, and we investigate, on the basis of this, the static dielectric response of a chain of hydrogen-bonded water molecules to an external field. To achieve this, we use a recently developed dipole lattice model that accurately captures the free energetics of nanopore water. In this model, the total energy of the system can be expressed as the sum of the effective interactions of chain ends and orientational defects. Neglecting these interactions, we essentially obtain the 1D Ising model, which allows us to derive analytical expressions for the free energy as a function of the total dipole moment and for the dielectric susceptibility. Our expressions, which agree very well with simulation results, provide the basis for the interpretation of future dielectric spectroscopy experiments on water-filled nanopore membranes.
Tightness of the Ising-Kac Model on the Two-Dimensional Torus
Hairer, Martin; Iberti, Massimo
2018-05-01
We consider the sequence of Gibbs measures of Ising models with Kac interaction defined on a periodic two-dimensional discrete torus near criticality. Using the convergence of the Glauber dynamic proven by Mourrat and Weber (Commun Pure Appl Math 70:717-812, 2017) and a method by Tsatsoulis and Weber employed in (arXiv:1609.08447 2016), we show tightness for the sequence of Gibbs measures of the Ising-Kac model near criticality and characterise the law of the limit as the Φ ^4_2 measure on the torus. Our result is very similar to the one obtained by Cassandro et al. (J Stat Phys 78(3):1131-1138, 1995) on Z^2, but our strategy takes advantage of the dynamic, instead of correlation inequalities. In particular, our result covers the whole critical regime and does not require the large temperature/large mass/small coupling assumption present in earlier results.
Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model
Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.
2018-04-01
While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.
International Nuclear Information System (INIS)
Tsallis, C.; Levy, S.V.F.
1979-05-01
Two different renormalization-group approaches are used to determine approximate solutions for the paramagnetic-ferromagnetic transition line of the square-lattice bond-dilute first-neighbour-interaction Ising model. (Author) [pt
Exact ground-state phase diagrams for the spin-3/2 Blume-Emery-Griffiths model
International Nuclear Information System (INIS)
Canko, Osman; Keskin, Mustafa; Deviren, Bayram
2008-01-01
We have calculated the exact ground-state phase diagrams of the spin-3/2 Ising model using the method that was proposed and applied to the spin-1 Ising model by Dublenych (2005 Phys. Rev. B 71 012411). The calculated, exact ground-state phase diagrams on the diatomic and triangular lattices with the nearest-neighbor (NN) interaction have been presented in this paper. We have obtained seven and 15 topologically different ground-state phase diagrams for J>0 and J 0 and J<0, respectively, the conditions for the existence of uniform and intermediate phases have also been found
Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model
International Nuclear Information System (INIS)
Hamer, C.J.; Barber, M.N.
1979-01-01
Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ
Schlittmeier, Sabine J; Weissgerber, Tobias; Kerber, Stefan; Fastl, Hugo; Hellbrück, Jürgen
2012-01-01
Background sounds, such as narration, music with prominent staccato passages, and office noise impair verbal short-term memory even when these sounds are irrelevant. This irrelevant sound effect (ISE) is evoked by so-called changing-state sounds that are characterized by a distinct temporal structure with varying successive auditory-perceptive tokens. However, because of the absence of an appropriate psychoacoustically based instrumental measure, the disturbing impact of a given speech or nonspeech sound could not be predicted until now, but necessitated behavioral testing. Our database for parametric modeling of the ISE included approximately 40 background sounds (e.g., speech, music, tone sequences, office noise, traffic noise) and corresponding performance data that was collected from 70 behavioral measurements of verbal short-term memory. The hearing sensation fluctuation strength was chosen to model the ISE and describes the percept of fluctuations when listening to slowly modulated sounds (f(mod) background sounds, the algorithm estimated behavioral performance data in 63 of 70 cases within the interquartile ranges. In particular, all real-world sounds were modeled adequately, whereas the algorithm overestimated the (non-)disturbance impact of synthetic steady-state sounds that were constituted by a repeated vowel or tone. Implications of the algorithm's strengths and prediction errors are discussed.
Fisher zeros in the Kallen-Lehmann approach to 3D Ising model
International Nuclear Information System (INIS)
Astorino, Marco; Canfora, Fabrizio; Giribet, Gaston
2009-01-01
The distribution of the Fisher zeros in the Kallen-Lehmann approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen-Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α and of the universal amplitude ratio Δ=A + /A - , within the 3.5% and 7% of the Monte Carlo predictions, respectively
Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
Ricateau, Hugo; Cugliandolo, Leticia F.; Picco, Marco
2018-01-01
We study, with numerical methods, the fractal properties of the domain walls found in slow quenches of the kinetic Ising model to its critical temperature. We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium.
Taskin, A A; Lavrov, A N; Ando, Yoichi
2003-06-06
In RBaCo2O5+x compounds (R is rare earth), a ferromagnetic-antiferromagnetic competition is accompanied by a giant magnetoresistance. We study the magnetization of detwinned GdBaCo2O5.5 single crystals and find a remarkable uniaxial anisotropy of Co3+ spins which is tightly linked with the chain oxygen ordering in GdO0.5 planes. Reflecting the underlying oxygen order, CoO2 planes also develop a spin-state order consisting of Co3+ ions in alternating rows of S=1 and S=0 states. The magnetic structure appears to be composed of weakly coupled ferromagnetic ladders with Ising-like moments, which gives a simple picture for magnetotransport phenomena.
Effective-field renormalization-group method for Ising systems
Fittipaldi, I. P.; De Albuquerque, D. F.
1992-02-01
A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.
Monte Carlo study of radiation-induced demagnetization using the two-dimensional Ising model
International Nuclear Information System (INIS)
Samin, Adib; Cao, Lei
2015-01-01
A simple radiation-damage model based on the Ising model for magnets is proposed to study the effects of radiation on the magnetism of permanent magnets. The model is studied in two dimensions using a Monte Carlo simulation, and it accounts for the radiation through the introduction of a localized heat pulse. The model exhibits qualitative agreement with experimental results, and it clearly elucidates the role that the coercivity and the radiation particle’s energy play in the process. A more quantitative agreement with experiment will entail accounting for the long-range dipole–dipole interactions and the crystalline anisotropy.
Monte Carlo study of radiation-induced demagnetization using the two-dimensional Ising model
Energy Technology Data Exchange (ETDEWEB)
Samin, Adib; Cao, Lei
2015-10-01
A simple radiation-damage model based on the Ising model for magnets is proposed to study the effects of radiation on the magnetism of permanent magnets. The model is studied in two dimensions using a Monte Carlo simulation, and it accounts for the radiation through the introduction of a localized heat pulse. The model exhibits qualitative agreement with experimental results, and it clearly elucidates the role that the coercivity and the radiation particle’s energy play in the process. A more quantitative agreement with experiment will entail accounting for the long-range dipole–dipole interactions and the crystalline anisotropy.
El-Showk, Sheer; Poland, David; Rychkov, Slava; Simmons-Duffin, David; Vichi, Alessandro
2014-01-01
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Delta_sigma=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.
Reduction of a Z(3) gauge theory on the flat lattices to the spin-1 BEG model
International Nuclear Information System (INIS)
Ananikian, N.S.; Shcherbakov, R.R.
1995-01-01
The Z(3) gauge model with double plaquette representation of the action on the flat triangular and square lattices is constructed. It is reduced to the spin-1 Blume-Emery-Griffiths (BEG) model. An Ising-type critical line of a second-order phase transition is found. ((orig.))
Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
Read, N.
2018-01-01
We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, which have mean zero and variance 1/|i -j | 2 σ, between the spins at sites i and j for all i ≠j . It is known that, for σ >1 , there is no phase transition at any nonzero temperature in this model. We prove rigorously that, for σ >3 /2 , any translation-covariant Newman-Stein metastate for the ground states (i.e., the frequencies with which distinct ground states are observed in finite-size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: One is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all σ >1 , that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for σ >3 /2 . In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values σ >1 /2 . Triviality of the metastate in bond-diluted power-law models for σ >1 is proved directly.
A spin exchange model for singlet fission
Yago, Tomoaki; Wakasa, Masanobu
2018-03-01
Singlet fission has been analyzed with the Dexter model in which electron exchange occurs between chromophores, conserving the spin for each electron. In the present study, we propose a spin exchange model for singlet fission. In the spin exchange model, spins are exchanged by the exchange interaction between two electrons. Our analysis with simple spin functions demonstrates that singlet fission is possible by spin exchange. A necessary condition for spin exchange is a variation in exchange interactions. We also adapt the spin exchange model to triplet fusion and triplet energy transfer, which often occur after singlet fission in organic solids.
International Nuclear Information System (INIS)
Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.
2009-01-01
An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.
Alécio, Raphael Cavalcante; Strečka, Jozef; Lyra, Marcelo L.
2018-04-01
The thermodynamic behavior of an Ising-Heisenberg triangular tube with Heisenberg intra-rung and Ising inter-rung interactions is exactly obtained in an external magnetic field within the framework of the transfer-matrix method. We report rigorous results for the temperature dependence of the magnetization, entropy, pair correlations and specific heat, as well as typical iso-entropic curves. The discontinuous field-driven ground-state phase transitions are reflected in some anomalous thermodynamic behavior as for instance a striking low-temperature peak of the specific heat and an enhanced magnetocaloric effect. It is demonstrated that the intermediate magnetization plateaus shrink in and the relevant sharp edges associated with the magnetization jump round off upon increasing temperature.
Shielding property for thermal equilibrium states in the quantum Ising model
Móller, N. S.; de Paula, A. L.; Drumond, R. C.
2018-03-01
We show that Gibbs states of nonhomogeneous transverse Ising chains satisfy a shielding property. Namely, whatever the fields on each spin and exchange couplings between neighboring spins are, if the field in one particular site is null, then the reduced states of the subchains to the right and to the left of this site are exactly the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, then we can guarantee a similar result only if the surface contains a single site. Already for an interface with two sites we show an example where the property does not hold. When it holds, however, we show that if a perturbation of the Hamiltonian parameters is done in one side of the lattice, then the other side is completely unchanged, with regard to both its equilibrium state and dynamics.
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
Mo, Qianxing
2010-01-29
ChIP-chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein-DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP-chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios. © 2010, The International Biometric Society.
Magnetization of the Ising model on the Sierpinski pastry-shell
Chame, Anna; Branco, N. S.
1992-02-01
Using a real-space renormalization group approach, we calculate the approximate magnetization in the Ising model on the Sierpinski Pastry-shell. We consider, as an approximation, only two regions of the fractal: the internal surfaces, or walls (sites on the border of eliminated areas), with coupling constants JS, and the bulk (all other sites), with coupling constants Jv. We obtain the mean magnetization of the two regions as a function of temperature, for different values of α= JS/ JV and different geometric parameters b and l. Curves present a step-like behavior for some values of b and l, as well as different universality classes for the bulk transition.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble....
Dimers and the Critical Ising Model on lattices of genus >1
International Nuclear Information System (INIS)
Costa-Santos, Ruben; McCoy, B.M.
2002-01-01
We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann surfaces
Approximating the Ising model on fractal lattices of dimension less than two
DEFF Research Database (Denmark)
Codello, Alessandro; Drach, Vincent; Hietanen, Ari
2015-01-01
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained...... with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also...
International Nuclear Information System (INIS)
Zhang Ang-Hui; Li Xiao-Wen; Su Gui-Feng; Zhang Yi
2015-01-01
We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series. (paper)
Kovacs effect in the one-dimensional Ising model: A linear response analysis
Ruiz-García, M.; Prados, A.
2014-01-01
We analyze the so-called Kovacs effect in the one-dimensional Ising model with Glauber dynamics. We consider small enough temperature jumps, for which a linear response theory has been recently derived. Within this theory, the Kovacs hump is directly related to the monotonic relaxation function of the energy. The analytical results are compared with extensive Monte Carlo simulations, and an excellent agreement is found. Remarkably, the position of the maximum in the Kovacs hump depends on the fact that the true asymptotic behavior of the relaxation function is different from the stretched exponential describing the relevant part of the relaxation at low temperatures.
Ising model with competing axial interactions in the presence of a field
International Nuclear Information System (INIS)
Yokoi, C.S.O.; Salinas, S.R.A.; Coutinho Filho, M.D.
1980-09-01
A layered Ising model is studied with competing interactions between nearest and next-nearest layers in the presence of a magnetic field. The analysis is carried out in the mean-field approximation with one effective field for each layer. The high-temperature region is studied analytically. The low-temperature region is studied numerically. T-H phase diagrams are constructed, which exhibit a variety of modulated phases, for various values of the ratio of the strength of the competing interactions. Numerical evidence of the devil's staircase behavior is found either as a function of temperature or applied magnetic field. (Author) [pt
New estimates on various critical/universal quantities of the 3d Ising model
International Nuclear Information System (INIS)
Hasenbusch, M.
1998-01-01
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude σ 0 in the critical law σ=ρ 0 t μ , and for the universal combination R - =σξ 2 . Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A + /A - , together with the exponent α, the nonsingular background of energy and specific heat at criticality, together with the exponent ν. There are also results for the universal combination f s ξ 3 , where f s is the singular part of the free energy. (orig.)
Numerical study of self-couplings in the broken phase of the lattice Ising model
International Nuclear Information System (INIS)
Munehisa, T.; Munehisa, Y.
1989-01-01
A Monte Carlo study of a one-component scalar Φ 4 model was made on a 10 4 hypercubic lattice in its Ising limit. We measured the renormalized mass and coupling of the three-point vertex in the spontaneously broken phase. By measuring them at non-zero momenta, we successfully settled problems caused by the finite vacuum expectation value of the scalar field. To suppress artificial fluctuation of observables, a uniform source was introduced. Our results are in good agreement with the one-loop relation between the vacuum expectation value, mass and the three-point coupling. (orig.)
Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.
2018-04-01
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.
Deviren, Seyma Akkaya
2017-02-01
In this research, we have investigated the magnetic properties of the spin-1 Ising model on the Shastry Sutherland lattice with the crystal field interaction by using the effective-field theory with correlations. The effects of the applied field on the magnetization are examined in detail in order to obtain the magnetization plateaus, thus different types of magnetization plateaus, such as 1/4, 1/3, 1/2, 3/5, 2/3 and 7/9 of the saturation, are obtained for strong enough magnetic fields (h). Magnetization plateaus exhibit single, triple, quintuplet and sextuple forms according to the interaction parameters, hence the magnetization plateaus originate from the competition between the crystal field (D) and exchange interaction parameters (J, J‧). The ground-state phase diagrams of the system are presented in three varied planes, namely (h/J, J‧/J), (h/J, D/J) and (D/J, J‧/J) planes. These phase diagrams display the Néel (N), collinear (C) and ferromagnetic (F) phases for certain values of the model parameters. The obtained results are in good agreement with some theoretical and experimental studies.
The Ising model for prediction of disordered residues from protein sequence alone
International Nuclear Information System (INIS)
Lobanov, Michail Yu; Galzitskaya, Oxana V
2011-01-01
Intrinsically disordered regions serve as molecular recognition elements, which play an important role in the control of many cellular processes and signaling pathways. It is useful to be able to predict positions of disordered residues and disordered regions in protein chains using protein sequence alone. A new method (IsUnstruct) based on the Ising model for prediction of disordered residues from protein sequence alone has been developed. According to this model, each residue can be in one of two states: ordered or disordered. The model is an approximation of the Ising model in which the interaction term between neighbors has been replaced by a penalty for changing between states (the energy of border). The IsUnstruct has been compared with other available methods and found to perform well. The method correctly finds 77% of disordered residues as well as 87% of ordered residues in the CASP8 database, and 72% of disordered residues as well as 85% of ordered residues in the DisProt database
Flocking with discrete symmetry: The two-dimensional active Ising model.
Solon, A P; Tailleur, J
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
Correspondence between spanning trees and the Ising model on a square lattice
Viswanathan, G. M.
2017-06-01
An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function T (z ) gives the spanning tree constant when evaluated at z =1 , while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function Z (K ) of the Ising model evaluated at the critical temperature K =Kc is related to T (1 ) . Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K ) s e c h 2 K ] 2=k exp[T (k )] , where k =2 tanh(2 K )s e c h (2 K ) . The identical Mahler measure connects the two seemingly disparate quantities T (z ) and Z (K ) . In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.
Stimulated wave of polarization in a one-dimensional Ising chain
International Nuclear Information System (INIS)
Lee, Jae-Seung; Khitrin, A.K.
2005-01-01
It is demonstrated that in a one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. This analytically solvable model illustrates mechanisms of quantum amplification and quantum measurement
Nuclear spin noise in the central spin model
Fröhling, Nina; Anders, Frithjof B.; Glazov, Mikhail
2018-05-01
We study theoretically the fluctuations of the nuclear spins in quantum dots employing the central spin model which accounts for the hyperfine interaction of the nuclei with the electron spin. These fluctuations are calculated both with an analytical approach using homogeneous hyperfine couplings (box model) and with a numerical simulation using a distribution of hyperfine coupling constants. The approaches are in good agreement. The box model serves as a benchmark with low computational cost that explains the basic features of the nuclear spin noise well. We also demonstrate that the nuclear spin noise spectra comprise a two-peak structure centered at the nuclear Zeeman frequency in high magnetic fields with the shape of the spectrum controlled by the distribution of the hyperfine constants. This allows for direct access to this distribution function through nuclear spin noise spectroscopy.
Environment overwhelms both nature and nurture in a model spin glass
Middleton, A. Alan; Yang, Jie
We are interested in exploring what information determines the particular history of the glassy long term dynamics in a disordered material. We study the effect of initial configurations and the realization of stochastic dynamics on the long time evolution of configurations in a two-dimensional Ising spin glass model. The evolution of nearest neighbor correlations is computed using patchwork dynamics, a coarse-grained numerical heuristic for temporal evolution. The dependence of the nearest neighbor spin correlations at long time on both initial spin configurations and noise histories are studied through cross-correlations of long-time configurations and the spin correlations are found to be independent of both. We investigate how effectively rigid bond clusters coarsen. Scaling laws are used to study the convergence of configurations and the distribution of sizes of nearly rigid clusters. The implications of the computational results on simulations and phenomenological models of spin glasses are discussed. We acknowledge NSF support under DMR-1410937 (CMMT program).
Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model
Kassebaum, Paul G.; Iannacchione, Germano S.
The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.
Q-deformed Grassmann field and the two-dimensional Ising model
International Nuclear Information System (INIS)
Bugrij, A.I.; Shadura, V.N.
1994-01-01
In this paper we construct the exact representation of the Ising partition function in form of the SL q (2,R)-invariant functional integral for the lattice free q-fermion field theory (q=-1). It is shown that the proposed method of q-fermionization allows one to re-express the partition function of the eight vertex model in external field through the functional integral with four-fermion interaction. For the construction of these representation we define a lattice (l,q,s)-deformed Grassmann bi spinor field and extend the Berezin integration rules for this field. At q = - 1, l = s 1 we obtain the lattice q-fermion field which allows to fermionize the two-dimensional Ising model. We show that Gaussian integral over (q,s)-Grassmann variables is expressed through the (q,s)-deformed Pfaffian which is equal to square root of the determinant of some matrix at q = ± 1, s = ±1. (author). 39 refs
The Ising model: from elliptic curves to modular forms and Calabi-Yau equations
International Nuclear Information System (INIS)
Bostan, A; Boukraa, S; Hassani, S; Zenine, N; Van Hoeij, M; Maillard, J-M; Weil, J-A
2011-01-01
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions of the susceptibility of the Ising model for n ≤ 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z 2 , F 2 , F 3 , L-tilde 3 can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-4 globally nilpotent linear differential operator is not reducible to this elliptic curve, modular form scheme. This operator is shown to actually correspond to a natural generalization of this elliptic curve, modular form scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected 4 F 3 hypergeometric function. This hypergeometric function can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back (square root extension), the corresponding Calabi-Yau fourth order differential operator having a symplectic differential Galois group SP(4,C). The mirror maps and higher order Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms, in particular an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2,Z) symmetry group.
Testing ground for fluctuation theorems: The one-dimensional Ising model
Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.
2018-04-01
In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.
Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
International Nuclear Information System (INIS)
Deng Dongling; Gu Shijian; Chen Jingling
2010-01-01
Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89 (2002) 060401] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.
CSIR Research Space (South Africa)
Britton, JW
2012-04-01
Full Text Available of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction , where 0=a=3 and di,j is the distance between spin pairs. These power laws correspond physically to infinite...
A hidden Ising model for ChIP-chip data analysis
Mo, Q.
2010-01-28
Motivation: Chromatin immunoprecipitation (ChIP) coupled with tiling microarray (chip) experiments have been used in a wide range of biological studies such as identification of transcription factor binding sites and investigation of DNA methylation and histone modification. Hidden Markov models are widely used to model the spatial dependency of ChIP-chip data. However, parameter estimation for these models is typically either heuristic or suboptimal, leading to inconsistencies in their applications. To overcome this limitation and to develop an efficient software, we propose a hidden ferromagnetic Ising model for ChIP-chip data analysis. Results: We have developed a simple, but powerful Bayesian hierarchical model for ChIP-chip data via a hidden Ising model. Metropolis within Gibbs sampling algorithm is used to simulate from the posterior distribution of the model parameters. The proposed model naturally incorporates the spatial dependency of the data, and can be used to analyze data with various genomic resolutions and sample sizes. We illustrate the method using three publicly available datasets and various simulated datasets, and compare it with three closely related methods, namely TileMap HMM, tileHMM and BAC. We find that our method performs as well as TileMap HMM and BAC for the high-resolution data from Affymetrix platform, but significantly outperforms the other three methods for the low-resolution data from Agilent platform. Compared with the BAC method which also involves MCMC simulations, our method is computationally much more efficient. Availability: A software called iChip is freely available at http://www.bioconductor.org/. Contact: moq@mskcc.org. © The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org.
Coupling between Spin and Charge Order Driven by Magnetic Field in Triangular Ising System LuFe2O4+δ
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Lei Ding
2018-02-01
Full Text Available We present a study of the magnetic-field effect on spin correlations in the charge ordered triangular Ising system LuFe2O4+δ through single crystal neutron diffraction. In the absence of a magnetic field, the strong diffuse neutron scattering observed below the Neel temperature (TN = 240 K indicates that LuFe2O4+δ shows short-range, two-dimensional (2D correlations in the FeO5 triangular layers, characterized by the development of a magnetic scattering rod along the 1/3 1/3 L direction, persisting down to 5 K. We also found that on top of the 2D correlations, a long range ferromagnetic component associated with the propagation vector k1 = 0 sets in at around 240 K. On the other hand, an external magnetic field applied along the c-axis effectively favours a three-dimensional (3D spin correlation between the FeO5 bilayers evidenced by the increase of the intensity of satellite reflections with propagation vector k2 = (1/3, 1/3, 3/2. This magnetic modulation is identical to the charge ordered superstructure, highlighting the field-promoted coupling between the spin and charge degrees of freedom. Formation of the 3D spin correlations suppresses both the rod-type diffuse scattering and the k1 component. Simple symmetry-based arguments provide a natural explanation of the observed phenomenon and put forward a possible charge redistribution in the applied magnetic field.
Statistically interacting quasiparticles in Ising chains
International Nuclear Information System (INIS)
Lu Ping; Vanasse, Jared; Piecuch, Christopher; Karbach, Michael; Mueller, Gerhard
2008-01-01
The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s = 1/2, 1. In the s = 1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s = 1/2 and to a system of six species of soliton pairs for s = 1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain
International Nuclear Information System (INIS)
Bobak, Andrej; Dely, Jan; Pokorny, Vladislav
2010-01-01
The effects of both an exchange anisotropy and a single-ion anisotropy on the magnetic susceptibility of the mixed spin-1 and spin- 1/2 Heisenberg model are investigated by the use of an Oguchi approximation. Particular emphasis is given to the simple cubic lattice with coordination number z = 6 for which the magnetic susceptibility is determined numerically. Anomalous behaviour in the thermal variation of the magnetic susceptibility in the low-temperature region is found due to the applied negative single-ion anisotropy field strength. Also, the difference between the behaviours of the magnetic susceptibility of the Heisenberg and Ising models is discussed.
Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model
Sousa, J. Ricardo de
A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.
DEFF Research Database (Denmark)
Høst-Madsen, Anders; Shah, Peter Jivan; Hansen, Torben
1987-01-01
Computer-simulation techniques are used to study the domain-growth kinetics of (2×1) ordering in a two-dimensional Ising model with nonconserved order parameter and with variable ratio α of next-nearest- and nearest-neighbor interactions. At zero temperature, persistent growth characterized...
Energy Technology Data Exchange (ETDEWEB)
Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)
2004-02-06
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.
Frozen into stripes: fate of the critical Ising model after a quench.
Blanchard, T; Picco, M
2013-09-01
In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.
Cluster-cluster correlations in the two-dimensional stationary Ising-model
International Nuclear Information System (INIS)
Klassmann, A.
1997-01-01
In numerical integration of the Cahn-Hillard equation, which describes Oswald rising in a two-phase matrix, N. Masbaum showed that spatial correlations between clusters scale with respect to the mean cluster size (itself a function of time). T. B. Liverpool showed by Monte Carlo simulations for the Ising model that the analogous correlations have a similar form. Both demonstrated that immediately around each cluster there is some depletion area followed by something like a ring of clusters of the same size as the original one. More precisely, it has been shown that the distribution of clusters around a given cluster looks like a sinus-curve decaying exponentially with respect to the distance to a constant value
International Nuclear Information System (INIS)
Kinoshita, Takehiro; Fujiyama, Shinya; Idogaki, Toshihiro; Tokita, Masahiko
2009-01-01
The non-equilibrium phase transition in a ferromagnetic Ising model is investigated by use of a new type of effective field theory (EFT) which correctly accounts for all the single-site kinematic relations by differential operator technique. In the presence of a time dependent oscillating external field, with decrease of the temperature the system undergoes a dynamic phase transition, which is characterized by the period averaged magnetization Q, from a dynamically disordered state Q = 0 to the dynamically ordered state Q ≠ 0. The results of the dynamic phase transition point T c determined from the behavior of the dynamic magnetization and the Liapunov exponent provided by EFT are improved than that of the standard mean field theory (MFT), especially for the one dimensional lattice where the standard MFT gives incorrect result of T c = 0 even in the case of zero external field.
Nonasymptotic form of the recursion relations of the three-dimensional Ising model
International Nuclear Information System (INIS)
Kozlovskii, M.P.
1989-01-01
Approximate recursion relations for the three-dimensional Ising model are obtained in the form of rapidly converging series. The representation of the recursion relations in the form of nonasymptotic series entails the abandonment of traditional perturbation theory based on a Gaussian measure density. The recursion relations proposed in the paper are used to calculate the critical exponent ν of the correlation length. It is shown that the difference form of the recursion relations leads, when higher non-Gaussian basis measures are used, to disappearance of a dependence of the critical exponent ν on s when s > 2 (s is the parameter of the division of the phase space into layers). The obtained results make it possible to calculate explicit expressions for the thermodynamic functions near the phase transition point
Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures
International Nuclear Information System (INIS)
Viteri, C. Ricardo; Tomita, Yu; Brown, Kenneth R.
2009-01-01
We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature.
Dynamical response of the Ising model to the time dependent magnetic field with white noise
Akıncı, Ümit
2018-03-01
The effect of the white noise in time dependent magnetic field on the dynamic behavior of the Ising model has been investigated within the effective field theory based on Glauber type of stochastic process. Discrete white noise has been chosen from both Gaussian and uniform probability distributions. Detailed investigation on probability distribution of dynamical order parameter results that, both type of noise distributions yield the same probability distribution related to the dynamical order parameter, namely Gaussian probability distribution. The variation of the parameters that describe the probability distribution of dynamical order parameter (mean value and standard deviation) with temperature and strength of the noise have been inspected. Also, it has been shown that, rising strength of the noise can induce dynamical phase transition in the system.
Finite-size-scaling analysis of subsystem data in the dilute Ising model
International Nuclear Information System (INIS)
Hennecke, M.
1993-01-01
Monte Carlo simulation results for the magnetization of subsystems of finite lattices are used to determine the critical temperature and a critical exponent of the simple-cubic Ising model with quenched site dilution, at a concentration of p=40%. Particular attention is paid to the effect of the finite size of the systems from which the subsystem results are obtained. This finiteness of the lattices involved is shown to be a source of large deviations of critical temperatures and exponents estimated from subsystem data from their values in the thermodynamic limit. By the use of different lattice sizes, the results T c (40%)=1.209±0.002 and ν(40%)=0.78±0.01 could be extrapolated
International Nuclear Information System (INIS)
Monthus, Cécile; Garel, Thomas
2012-01-01
To avoid the complicated topology of surviving clusters induced by standard strong disorder RG in dimension d > 1, we introduce a modified procedure called ‘boundary strong disorder RG’ where the order of decimations is chosen a priori. We apply this modified procedure numerically to the random transverse field Ising model in dimension d = 2. We find that the location of the critical point, the activated exponent ψ ≃ 0.5 of the infinite-disorder scaling, and the finite-size correlation exponent ν FS ≃ 1.3 are compatible with the values obtained previously using standard strong disorder RG. Our conclusion is thus that strong disorder RG is very robust with respect to changes in the order of decimations. In addition, we analyze the RG flows within the two phases in more detail, to show explicitly the presence of various correlation length exponents: we measure the typical correlation exponent ν typ ≃ 0.64 for the disordered phase (this value is very close to the correlation exponent ν pure Q (d=2)≅0.6 3 of the pure two-dimensional quantum Ising model), and the typical exponent ν h ≃ 1 for the ordered phase. These values satisfy the relations between critical exponents imposed by the expected finite-size scaling properties at infinite-disorder critical points. We also measure, within the disordered phase, the fluctuation exponent ω ≃ 0.35 which is compatible with the directed polymer exponent ω DP (1+1)= 1/3 in (1 + 1) dimensions. (paper)
Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt
2014-08-01
We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples.
New Spin Foam Models of Quantum Gravity
Miković, A.
We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.
Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory
Directory of Open Access Journals (Sweden)
T. K. Das
2014-01-01
Full Text Available With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model or global dynamics (e.g., the Ising model have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.
Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs
Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.
2018-04-01
Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.
Heisenberg spin glass experiments and the chiral ordering scenario
International Nuclear Information System (INIS)
Campbell, Ian A.; Petit, Dorothee C.M.C.
2010-01-01
An overview is given of experimental data on Heisenberg spin glass materials so as to make detailed comparisons with numerical results on model Heisenberg spin glasses, with particular reference to the chiral driven ordering transition scenario due to Kawamura and collaborators. On weak anisotropy systems, experiments show critical exponents which are very similar to those estimated numerically for the model Heisenberg chiral ordering transition but which are quite different from those at Ising spin glass transitions. Again on weak anisotropy Heisenberg spin glasses, experimental torque data show well defined in-field transverse ordering transitions up to strong applied fields, in contrast to Ising spin glasses where fields destroy ordering. When samples with stronger anisotropies are studied, critical and in-field behavior tend progressively towards the Ising limit. It can be concluded that the essential physics of laboratory Heisenberg spin glasses mirrors that of model Heisenberg spin glasses, where chiral ordering has been demonstrated numerically. (author)
Spin-spin correlations in the tt'-Hubbard model
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Husslein, T.; Newns, D.M.; Mattutis, H.G.; Pattnaik, P.C.; Morgenstern, I.; Singer, J.M.; Fettes, W.; Baur, C.
1994-01-01
We present calculations of the tt'-Hubbard model using Quantum Monte Carlo techniques. The parameters are chosen so that the van Hove Singularity in the density of states and the Fermi level coincide. We study the behaviour of the system with increasing Hubbard interaction U. Special emphasis is on the spin-spin correlation (SSC). Unusual behaviour for large U is observed there and in the momentum distribution function (n(q)). (orig.)
International Nuclear Information System (INIS)
Ertaş Mehmet; Keskin Mustafa
2013-01-01
Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin (2, 5/2) Ising system for the antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the bilayer square lattice under a time varying (sinusoidal) magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic (FM/FM) and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions. (general)
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Finite-range-scaling analysis of metastability in an Ising model with long-range interactions
International Nuclear Information System (INIS)
Gorman, B.M.; Rikvold, P.A.; Novotny, M.A.
1994-01-01
We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the Nx∞ quasi-one-dimensional Ising model. Using the field theory, we find the analytic continuation f of the free energy across the first-order transition, assuming that the system escapes the metastable state by the nucleation of noninteracting droplets. We find that corrections to the field dependence are substantial, and, by solving the Euler-Lagrange equation for the model numerically, we have verified the form of the free-energy cost of nucleation, including the first correction. In the transfer-matrix method, we associate with the subdominant eigenvectors of the transfer matrix a complex-valued ''constrained'' free-energy density f α computed directly from the matrix. For the eigenvector with an associated magnetization most strongly opposed to the applied magnetic field, f α exhibits finite-range scaling behavior in agreement with f over a wide range of temperatures and fields, extending nearly to the classical spinodal. Some implications of these results for numerical studies of metastability are discussed
On the TAP Free Energy in the Mixed p-Spin Models
Chen, Wei-Kuo; Panchenko, Dmitry
2018-05-01
Thouless et al. (Phys Mag 35(3):593-601, 1977), derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy on the extended configuration space of local magnetizations with an Onsager correction term. In the setting of mixed p-spin models with Ising spins, we prove that the free energy can indeed be written as the supremum of the TAP free energy over the space of local magnetizations whose Edwards-Anderson order parameter (self-overlap) is to the right of the support of the Parisi measure. Furthermore, for generic mixed p-spin models, we prove that the free energy is equal to the TAP free energy evaluated on the local magnetization of any pure state.
Quenched random-bond ising ferromagnet
International Nuclear Information System (INIS)
Sarmento, E.F.; Honmura, R.; Tsallis, C.; Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro)
1984-01-01
A effective-field framework which, without mathematical complexities, enables the calculation of the phase diagram (and magnetization) associated with a quenched bond-mixed spin - 1/2 Ising model in an anisotropic simple cubic lattice have been recently introduced. The case corresponding to anisotropic coupling constants but isotropic concentrations was discussed in detail. Herein the case corresponding to isotropic coupling constants but anisotropic concentrations is discussed. A certain amount of interesting phase diagrams are exhibited; whenever comparison with available data is possible, the present results provide a satisfactory qualitative (and to a certain extent quantitative) agreement. (Author) [pt
Exact ground-state phase diagrams for the spin-3/2 Blume-Emery-Griffiths model
Energy Technology Data Exchange (ETDEWEB)
Canko, Osman; Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Deviren, Bayram [Institute of Science, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr
2008-05-15
We have calculated the exact ground-state phase diagrams of the spin-3/2 Ising model using the method that was proposed and applied to the spin-1 Ising model by Dublenych (2005 Phys. Rev. B 71 012411). The calculated, exact ground-state phase diagrams on the diatomic and triangular lattices with the nearest-neighbor (NN) interaction have been presented in this paper. We have obtained seven and 15 topologically different ground-state phase diagrams for J>0 and J<0, respectively, on the diatomic lattice and have found the conditions for the existence of uniform and intermediate or non-uniform phases. We have also constructed the exact ground-state phase diagrams of the model on the triangular lattice and found 20 and 59 fundamental phase diagrams for J>0 and J<0, respectively, the conditions for the existence of uniform and intermediate phases have also been found.
Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
Abeling, Nils; Kehrein, Stefan
The recently discovered Dynamical Phase Transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this talk we present the extension of the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0 . This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. This work was supported through CRC SFB 1073 (Project B03) of the Deutsche Forschungsgemeinschaft (DFG).
Fang, Wen; Wang, Jun
2013-09-01
We develop a financial market model using an Ising spin system on a Sierpinski carpet lattice that breaks the equal status of each spin. To study the fluctuation behavior of the financial model, we present numerical research based on Monte Carlo simulation in conjunction with the statistical analysis and multifractal analysis of the financial time series. We extract the multifractal spectra by selecting various lattice size values of the Sierpinski carpet, and the inverse temperature of the Ising dynamic system. We also investigate the statistical fluctuation behavior, the time-varying volatility clustering, and the multifractality of returns for the indices SSE, SZSE, DJIA, IXIC, S&P500, HSI, N225, and for the simulation data derived from the Ising model on the Sierpinski carpet lattice. A numerical study of the model’s dynamical properties reveals that this financial model reproduces important features of the empirical data.
Directory of Open Access Journals (Sweden)
D.Ivaneyko
2005-01-01
Full Text Available We apply numerical simulations to study of the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio Γ+/Γ- for the magnetic susceptibility critical amplitudes. Our estimate Γ+/Γ- = 1.67 ± 0.15 is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh, E-mail: far75m@yandex.ru, E-mail: farrukh.m@uaeu.ac.ae [International Islamic University Malaysia, Department of Computational and Theoretical Sciences, Faculty of Science (Malaysia); Barhoumi, Abdessatar, E-mail: abdessatar.barhoumi@ipein.rnu.tn [Carthage University, Department of Mathematics, Nabeul Preparatory Engineering Institute (Tunisia); Souissi, Abdessatar, E-mail: s.abdessatar@hotmail.fr [Carthage University, Department of Mathematics, Marsa Preparatory Institute for Scientific and Technical Studies (Tunisia)
2016-12-15
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.
Test of quantum thermalization in the two-dimensional transverse-field Ising model.
Blaß, Benjamin; Rieger, Heiko
2016-12-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
The square lattice Ising model on the rectangle II: finite-size scaling limit
Hucht, Alfred
2017-06-01
Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor. 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L, M\\to∞ , T\\to Tc , with fixed temperature scaling variable x\\propto(T/Tc-1)M and fixed aspect ratio ρ\\propto L/M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T=Tc we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys. B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen. 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.
Phase transitions in an Ising model for monolayers of coadsorbed atoms
International Nuclear Information System (INIS)
Lee, H.H.; Landau, D.P.
1979-01-01
A Monte Carlo method is used to study a simple S=1 Ising (lattice-gas) model appropriate for monolayers composed of two kinds of atoms on cubic metal substrates H = K/sub nn/ Σ/sub nn/ S 2 /sub i/zS 2 /sub j/z + J/sub nnn/ Σ/sub nnn/ S/sub i/zS/sub j/z + Δ Σ/sub i/ S 2 /sub i/z (where nn denotes nearest-neighbor and nnn next-nearest-neighbor pairs). The phase diagram is determined over a wide range of Δ and T for K/sub nn//J/sub nnn/=1/4. For small (or negative) Δ we find an antiferromagnetic 2 x 1 ordered phase separated from the disordered state by a line of second-order phase transitions. The 2 x 1 phase is separated by a line of first-order transitions from a c (2 x 2) phase which appears for larger Δ. The 2 x 1 and c (2 x 2) phases become simultaneously critical at a bicritical point and the phase boundary of the c (2 x 2) → disordered transition shows a tricritical point
Test of quantum thermalization in the two-dimensional transverse-field Ising model
Blaß, Benjamin; Rieger, Heiko
2016-01-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems. PMID:27905523
High order Fuchsian equations for the square lattice Ising model: χ-tilde(5)
International Nuclear Information System (INIS)
Bostan, A; Boukraa, S; Guttmann, A J; Jensen, I; Hassani, S; Zenine, N; Maillard, J-M
2009-01-01
We consider the Fuchsian linear differential equation obtained (modulo a prime) for χ-tilde (5) , the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of χ-tilde (1) and χ-tilde (3) can be removed from χ-tilde (5) and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth-order linear differential operator occurs as the left-most factor of the 'depleted' differential operator and it is shown to be equivalent to the symmetric fourth power of L E , the linear differential operator corresponding to the elliptic integral E. This result generalizes what we have found for the lower order terms χ-tilde (3) and χ-tilde (4) . We conjecture that a linear differential operator equivalent to a symmetric (n - 1) th power of L E occurs as a left-most factor in the minimal order linear differential operators for all χ-tilde (n) 's
Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory
International Nuclear Information System (INIS)
Deviren, Bayram; Canko, Osman; Keskin, Mustafa
2010-01-01
Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 . (general)
Fluctuation relations in non-equilibrium stationary states of Ising models
Energy Technology Data Exchange (ETDEWEB)
Piscitelli, A; Gonnella, G [Dipartimento di Fisica, Universita di Bari and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Amendola 173, 70126 Bari (Italy); Corberi, F [Dipartimento di Matematica ed Informatica, via Ponte don Melillo, Universita di Salerno, 84084 Fisciano (Italy); Pelizzola, A [Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Sezione di Torino, and CNISM, Politecnico di Torino, c. Duca degli Abruzzi 24, 10129 Torino (Italy)
2009-01-15
Fluctuation relations for the entropy production in non-equilibrium stationary states of Ising models are investigated by means of Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external driving will be studied. In the first case, considering different kinetic rules and couplings with the baths, the behaviors of the probability distributions of the heat exchanged in time {tau} with the thermostats, both in the disordered phase and in the low temperature phase, are discussed. The fluctuation relation is always followed in the large {tau} limit and deviations from linear response theory are observed. Finite {tau} corrections are shown to obey a scaling behavior. In the other case the system is in contact with a single heat bath, but work is done by shearing it. Also for this system, using the statistics collected for the mechanical work we show the validity of the fluctuation relation and the preasymptotic corrections behave analogously to those for the case with two baths.
Coevolution of Glauber-like Ising dynamics and topology
Mandrà, Salvatore; Fortunato, Santo; Castellano, Claudio
2009-11-01
We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.
Degenerate Ising model for atomistic simulation of crystal-melt interfaces
International Nuclear Information System (INIS)
Schebarchov, D.; Schulze, T. P.; Hendy, S. C.
2014-01-01
One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level
Degenerate Ising model for atomistic simulation of crystal-melt interfaces
Energy Technology Data Exchange (ETDEWEB)
Schebarchov, D., E-mail: Dmitri.Schebarchov@gmail.com [University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW (United Kingdom); Schulze, T. P., E-mail: schulze@math.utk.edu [Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300 (United States); Hendy, S. C. [The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington 6140 (New Zealand); Department of Physics, University of Auckland, Auckland 1010 (New Zealand)
2014-02-21
One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level.
Quantum Ising chains with boundary fields
International Nuclear Information System (INIS)
Campostrini, Massimo; Vicari, Ettore; Pelissetto, Andrea
2015-01-01
We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the boundaries of the chain that have the same strength and that are aligned in the same or in the opposite direction. We derive analytic expressions for the gap in all phases for large values of the chain length L, as a function of the boundary field strength. We also investigate the behaviour of the chain in the quantum ferromagnetic phase for oppositely aligned fields, focusing on the magnet-to-kink transition that occurs at a finite value of the magnetic field strength. At this transition we compute analytically the finite-size crossover functions for the gap, the magnetisation profile, the two-point correlation function, and the density of fermionic modes. As the magnet-to-kink transition is equivalent to the wetting transition in two-dimensional classical Ising models, our results provide new analytic predictions for the finite-size behaviour of Ising systems in a strip geometry at this transition. (paper)
Broken symmetry in the mean field theory of the ising spin glass: replica way and no replica way
International Nuclear Information System (INIS)
De Dominicis, C.
1983-06-01
We review the type of symmetry breaking involved in the solution discovered by Parisi and in the static derivation of the solution first introduced via dynamics by Sompolinsky. We turn to a formulation of the problem due to Thouless, Anderson and Palmer (TAP) that put a set of equations for the magnetization. A probability law for the magnetization is then built. We consider two cases: (i) a canonical distribution which is shown to give indentical results to the Hamiltonian formulation under a weak and physical assumption and (ii) a white distribution characterized by two matrices and a response. We show what symmetry breaking is necessary to recover Sompolinsky free energy. In section III we supplement replica indices in the Hamiltonian approach by ''time'' indices ans show in particular that the analytic continuation involved in Sompolinsky's equilibrium derivation, is trying to mimick a translational symmetry breaking in ''time'' that incorporates Sompolinsky's ansatz of a long time scale sequence. In section IV we apply the same treatment to the white average approach and show that, replicas can be altogether discorded and replaced by ''time''. Finally, we briefly discuss the attribution of distinct answers for the standard spin glass order parameter depending on the physical situation: equilibrium or non equilibrium associated with canonical or white (non canonical) initial conditions and density matrices
Exact solution of the Ising model in a fully frustrated two-dimensional lattice
International Nuclear Information System (INIS)
Silva, N.R. da; Medeiros e Silva Filho, J.
1983-01-01
A straightforward extension of the Onsager method allows us to solve exactly the Ising problem in a fully frustated square lattice in the absence of external magnetic field. It is shown there is no singularity in the thermodynamic functions for non-zero temperature. (Author) [pt
From tricritical Ising to critical Ising by thermodynamic Bethe ansatz
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1991-01-01
A simple factorized scattering theory is suggested for the massless Goldstone fermions of the trajectory flowing from the tricritical Ising fixed point to the critical Ising one. The thermodynamic Bethe ansatz approach is applied to this scattering theory to support its interpretation both analytically and numerically. As a generalization a sequence of massless TBA systems is proposed which seems relevant for the trajectories interpolating between two successive minimal CFT models M p and M p-1 . (orig.)
Study of an Ising model with competing long- and short-range interactions
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Loew, U.; Emery, V.J.; Fabricius, K.; Kivelson, S.A.
1994-01-01
A classical spin-one lattice gas model is used to study the competition between short-range ferromagnetic coupling and long-range antiferromagnetic Coulomb interactions. The model is a coarse-grained representation of frustrated phase separation in high-temperature superconductors. The ground states are determined for the complete range of parameters by using a combination of numerical and analytical techniques. The crossover between ferromagnetic and antiferromagnetic states proceeds via a rich structure of highly symmetric striped and checkerboard phases. There is no devil's staircase behavior because mixtures of stripes with different period phase separate
Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study
Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.
2017-08-01
The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.
International Nuclear Information System (INIS)
Colomo, F.; Mussardo, G.
1992-01-01
In this paper, the authors compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov's RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. The authors use finite-size techniques to compare their results with the numerical data obtained by the truncated conformal space approach and find good agreement
Phase diagram with an enhanced spin-glass region of the mixed Ising-XY magnet LiHo_{x}Er_{1-x}F_{4}
DEFF Research Database (Denmark)
Piatek, J. O.; Dalla Piazza, B.; Nikseresht, N.
2013-01-01
We present the experimental phase diagram of LiHoxEr1-xF4, a dilution series of dipolar-coupled model magnets. The phase diagram was determined using a combination of ac susceptibility and neutron scattering. Three unique phases in addition to the Ising ferromagnet LiHoF4 and the XY antiferromagn...
Mills, Kyle; Tamblyn, Isaac
2018-03-01
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4 ×4 Ising model. Using its success at this task, we motivate the study of the larger 8 ×8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration.
Moore, M A; Katzgraber, Helmut G
2014-10-01
Starting from preferences on N proposed policies obtained via questionnaires from a sample of the electorate, an Ising spin-glass model in a field can be constructed from which a political party could find the subset of the proposed policies which would maximize its appeal, form a coherent choice in the eyes of the electorate, and have maximum overlap with the party's existing policies. We illustrate the application of the procedure by simulations of a spin glass in a random field on scale-free networks.
Inozemtsev's hyperbolic spin model and its related spin chain
International Nuclear Information System (INIS)
Barba, J.C.; Finkel, F.; Gonzalez-Lopez, A.; Rodriguez, M.A.
2010-01-01
In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.
International Nuclear Information System (INIS)
Bouttier, J; Francesco, P Di; Guitter, E
2007-01-01
We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations
Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: A numerical test
International Nuclear Information System (INIS)
Astorino, Marco; Canfora, Fabrizio; Martinez, Cristian; Parisi, Luca
2008-01-01
A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatures. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the Monte Carlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte Carlo results by introducing a more general duality breaking is shortly discussed
Ising game: Nonequilibrium steady states of resource-allocation systems
Xin, C.; Yang, G.; Huang, J. P.
2017-04-01
Resource-allocation systems are ubiquitous in the human society. But how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model. Because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory, here we combine the Ising model with the market-directed resource-allocation game, yielding an Ising game. Based on the Ising game, we show theoretical, simulative and experimental evidences for a formula, which offers a clear expression of nonequilibrium steady states (NESSs). Interestingly, the formula also reveals a convertible relationship between the external field (exogenous factor) and resource ratio (endogenous factor), and a class of saturation as the external field exceeds certain limits. This work suggests that the Ising game could be a suitable model for studying external-field effects on resource-allocation systems, and it could provide guidance both for seeking more relations between NESSs and equilibrium states and for regulating human systems by choosing NESSs appropriately.
Inverse Ising problem in continuous time: A latent variable approach
Donner, Christian; Opper, Manfred
2017-12-01
We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
LeVine, Michael V; Weinstein, Harel
2015-05-01
In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular "action at a distance" is termed allostery . Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.
Efficient micromagnetic modelling of spin-transfer torque and spin-orbit torque
Abert, Claas; Bruckner, Florian; Vogler, Christoph; Suess, Dieter
2018-05-01
While the spin-diffusion model is considered one of the most complete and accurate tools for the description of spin transport and spin torque, its solution in the context of dynamical micromagnetic simulations is numerically expensive. We propose a procedure to retrieve the free parameters of a simple macro-spin like spin-torque model through the spin-diffusion model. In case of spin-transfer torque the simplified model complies with the model of Slonczewski. A similar model can be established for the description of spin-orbit torque. In both cases the spin-diffusion model enables the retrieval of free model parameters from the geometry and the material parameters of the system. Since these parameters usually have to be determined phenomenologically through experiments, the proposed method combines the strength of the diffusion model to resolve material parameters and geometry with the high performance of simple torque models.
International Nuclear Information System (INIS)
Boulatov, D.V.; Kazakov, V.A.
1987-01-01
We investigate the critical properties of a recently proposed exactly soluble Ising model on a planar random dynamical lattice representing a regularization of the zero-dimensional string with internal fermions. The sum over all lattices gives rise to a new quantum degree of freedom - fluctuation of the metric. The whole system of critical exponents is found: α = -1, β = 1/2, γ = 2, δ = 5, v . D = 3. To test the universality we have used the planar graphs with the coordination number equal to 4 (Φ 4 theory graphs) as well as with the equal to 3 (Φ 3 theory graphs or triangulations). The critical exponents coincide for both cases. (orig.)
International Nuclear Information System (INIS)
Dahmen, Bernd
1994-01-01
A systematic method to obtain strong coupling expansions for scattering quantities in hamiltonian lattice field theories is presented. I develop the conceptual ideas for the case of the hamiltonian field theory analogue of the Ising model, in d space and one time dimension. The main result is a convergent series representation for the scattering states and the transition matrix. To be explicit, the special cases of d=1 and d=3 spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed. ((orig.))
Experimental tests of proton spin models
International Nuclear Information System (INIS)
Ramsey, G.P.; Argonne National Lab., IL
1989-01-01
We have developed models for the spin-weighted quark and gluon distribution in a longitudinally polarized proton. The model parameters are determined from current algebra sum rules and polarized deep-inelastic scattering data. A number of different scenarios are presented for the fraction of spin carried the constituent parton distributions. A possible long-range experimental program is suggested for measuring various hard scattering processes using polarized lepton and proton beams. With the knowledge gained from these experiments, we can begin to understand the parton contributions to the proton spin. 28 refs., 5 figs
Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
Energy Technology Data Exchange (ETDEWEB)
Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida (Algeria); Guttmann, A J; Jensen, I [ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Nickel, B [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)], E-mail: boukraa@mail.univ-blida.dz, E-mail: tonyg@ms.unimelb.edu.au, E-mail: I.Jensen@ms.unimelb.edu.au, E-mail: maillard@lptmc.jussieu.fr, E-mail: maillard@lptl.jussieu.fr, E-mail: njzenine@yahoo.com
2008-11-14
We calculate very long low- and high-temperature series for the susceptibility {chi} of the square lattice Ising model as well as very long series for the five-particle contribution {chi}{sup (5)} and six-particle contribution {chi}{sup (6)}. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for {chi} (low- and high-temperature regimes), {chi}{sup (5)} and {chi}{sup (6)} are now extended to 2000 terms. In addition, for {chi}{sup (5)}, 10 000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by {chi}{sup (5)} modulo a prime. A diff-Pade analysis of the 2000 terms series for {chi}{sup (5)} and {chi}{sup (6)} confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of {chi}{sup (5)} and the (as yet unknown) ODE of {chi}{sup (6)} are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of {chi}{sup (5)}, and w{sup 2} = 1/8 for the ODE of {chi}{sup (6)}, which are not singularities of the 'physical' {chi}{sup (5)} and {chi}{sup (6)}, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for {chi}{sup (5)} (and {chi}{sup (6)}) combined with the corresponding long series for the full susceptibility {chi} yields previously conjectured singularities in some {chi}{sup (n)}, n {>=} 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the {chi}{sup (n)} leading to the known power-law critical behaviour occurring in
Damage spreading at the corner-filling transition in the two-dimensional Ising model
International Nuclear Information System (INIS)
Rubio Puzzo, M Leticia; Albano, Ezequiel V
2007-01-01
The propagation of damage on the square Ising lattice with a corner geometry is studied by means of Monte Carlo simulations. By imposing free boundary conditions at which competing boundary magnetic fields ± h are applied, the system undergoes a filling transition at a temperature T f (h) lower than the Onsager critical temperature T C . The competing fields cause the formation of two magnetic domains with opposite orientation of the magnetization, separated by an interface that for T larger than T f (h) (but T C ) runs along the diagonal of the sample that connects the corners where the magnetic fields of different orientation meet. Also, for T f (h) this interface is localized either close to the corner where the magnetic field is positive or close to the opposite one, with the same probability. It is found that, just at T = T f (h), the damage initially propagates along the interface of the competing domains, according to a power law given by D(t) ∝ t η . The value obtained for the dynamic exponent (η* = 0.89(1)) is in agreement with that corresponding to the wetting transition in the slit geometry (Abraham model) given by η WT = 0.91(1). However, for later times the propagation crosses to a new regime such as η** = 0.40(2), which is due to the propagation of the damage into the bulk of the magnetic domains. This result can be understood as being due to the constraints imposed on the propagation of damage by the corner geometry of the system that cause healing at the corners where the interface is attached. The critical points for the damage-spreading transition (T D (h)) are evaluated by extrapolation to the thermodynamic limit by using a finite-size scaling approach. Considering error bars, an overlap between the filling and the damage-spreading transitions is found, such that T f (h) = T D (h). The probability distribution of the damage average position P(l 0 D ) and that of the interface between magnetic domains of different orientation P(l 0 ) are
2013-01-01
This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can - within a single book - obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated
From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves
Directory of Open Access Journals (Sweden)
Salah Boukraa
2007-10-01
Full Text Available We recall the form factors $f^(j_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a "Russian-doll" nesting, and a decomposition of the linear differential operators as a direct sum of operators (equivalent to symmetric powers of the differential operator of the complete elliptic integral $E$. The scaling limit of these differential operators breaks the direct sum structure but not the "Russian doll" structure, the "scaled" linear differential operators being no longer Fuchsian. We then introduce some multiple integrals of the Ising class expected to have the same singularities as the singularities of the $n$-particle contributions $chi^{(n}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equations satisfied by these multiple integrals for $n = 1, 2, 3, 4$ and, only modulo a prime, for $n = 5$ and 6, thus providing a large set of (possible new singularities of the $chi^{(n}$. We get the location of these singularities by solving the Landau conditions. We discuss the mathematical, as well as physical, interpretation of these new singularities. Among the singularities found, we underline the fact that the quadratic polynomial condition $1 + 3w + 4w^2 = 0$, that occurs in the linear differential equation of $chi^{(3}$, actually corresponds to the occurrence of complex multiplication for elliptic curves. The interpretation of complex multiplication for elliptic curves as complex fixed points of generators of the exact renormalization group is sketched. The other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting a geometric interpretation in terms of more general (motivic mathematical structures beyond the theory of elliptic curves. The scaling limit of the (lattice
Quantum influence in the criticality of the spin- {1}/{2} anisotropic Heisenberg model
Ricardo de Sousa, J.; Araújo, Ijanílio G.
1999-07-01
We study the spin- {1}/{2} anisotropic Heisenberg antiferromagnetic model using the effective field renormalization group (EFRG) approach. The EFRG method is illustrated by employing approximations in which clusters with one ( N'=1) and two ( N=2) spins are used. The dependence of the critical temperature Tc (ferromagnetic-F case) and TN (antiferromagnetic-AF case) and thermal critical exponent, Yt, are obtained as a function of anisotropy parameter ( Δ) on a simple cubic lattice. We find that, in our results, TN is higher than Tc for the quantum anisotropic Heisenberg limit and TN= Tc for the Ising and quantum XY limits. We have also shown that the thermal critical exponent Yt for the isotropic Heisenberg model shows a small dependence on the type of interaction (F or AF) due to finite size effects.
Discrete approximations to vector spin models
Energy Technology Data Exchange (ETDEWEB)
Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)
2011-11-25
We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
Discrete approximations to vector spin models
International Nuclear Information System (INIS)
Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A
2011-01-01
We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
International Nuclear Information System (INIS)
Žukovič, Milan; Hristopulos, Dionissios T
2009-01-01
A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the N c -state Potts model, each point is assigned to one of N c classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of
Žukovič, Milan; Hristopulos, Dionissios T.
2009-02-01
A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the Nc-state Potts model, each point is assigned to one of Nc classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of
Percolation and spin glass transition
International Nuclear Information System (INIS)
Sadiq, A.; Tahir-Kheli, R.A.; Wortis, M.; Bhatti, N.A.
1980-10-01
The behaviour of clusters of curved and normal plaquette particles in a bond random, +-J, Ising model is studied in finite square and triangular lattices. Computer results for the concentration of antiferromagnetic bonds when percolating clusters first appears are found to be close to those reported for the occurrence and disappearance of spin glass phases in these systems. (author)
Semiconductor of spinons: from Ising band insulator to orthogonal band insulator.
Farajollahpour, T; Jafari, S A
2018-01-10
We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the 'ARPES-dark' state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.
Semiconductor of spinons: from Ising band insulator to orthogonal band insulator
Farajollahpour, T.; Jafari, S. A.
2018-01-01
We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the ‘ARPES-dark’ state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.
Jiménez, Andrea
2014-02-01
We study the unexpected asymptotic behavior of the degeneracy of the first few energy levels in the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. There are strong mathematical and physical reasons to expect that the number of ground states (i.e., degeneracy) of the antiferromagnetic Ising model on the triangulations of a fixed closed Riemann surface is exponential in the number of vertices. In the set of plane triangulations, the degeneracy equals the number of perfect matchings of the geometric duals, and thus it is exponential by a recent result of Chudnovsky and Seymour. From the physics point of view, antiferromagnetic triangulations are geometrically frustrated systems, and in such systems exponential degeneracy is predicted. We present results that contradict these predictions. We prove that for each closed Riemann surface S of positive genus, there are sequences of triangulations of S with exactly one ground state. One possible explanation of this phenomenon is that exponential degeneracy would be found in the excited states with energy close to the ground state energy. However, as our second result, we show the existence of a sequence of triangulations of a closed Riemann surface of genus 10 with exactly one ground state such that the degeneracy of each of the 1st, 2nd, 3rd and 4th excited energy levels belongs to O( n), O( n 2), O( n 3) and O( n 4), respectively.
Emergent Ising degrees of freedom above a double-stripe magnetic ground state
Zhang, Guanghua; Flint, Rebecca
2017-12-01
Double-stripe magnetism [Q =(π /2 ,π /2 )] has been proposed as the magnetic ground state for both the iron-telluride and BaTi2Sb2O families of superconductors. Double-stripe order is captured within a J1-J2-J3 Heisenberg model in the regime J3≫J2≫J1 . Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π ,π ) . Because the ground state is fourfold degenerate, modulo rotations in spin space, only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.
Tadić, Bosiljka
2018-03-01
We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other
Thermal contact through a two-temperature kinetic Ising chain
Bauer, M.; Cornu, F.
2018-05-01
We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different temperatures and kinetic parameters on alternating sites. The inhomogeneity of the kinetic parameter is a novelty with respect to the model of Racz and Zia (1994 Phys. Rev. E 49 139), and we exhibit its influence upon the stationary non equilibrium values of the two-spin correlations at any distance. By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.
Ising-type anisotropy and spin state transitions in GdBaCo2O5.5 from first-principles calculations
International Nuclear Information System (INIS)
Pardo, V.; Baldomir, D.; Castro, J.; Iglesias, M.; Arias, J.E.
2007-01-01
Ising-type behaviour of GdBaCo 2 O 5.5 is analyzed from first principles calculations of the electronic structure of the material. The variations in its magnetic anisotropy properties in the different possible magnetic configurations is analyzed. A possible metallic phase is studied and an analysis of the electronic structure of the Co 3+ ions in that phase is presented
Restrictions on modeling spin injection by resistor networks
Rashba, Emmanuel
2008-01-01
Because of the technical difficulties of solving spin transport equations in inhomogeneous systems, different resistor networks are widely applied for modeling spin transport. By comparing an analytical solution for spin injection across a ferromagnet - paramagnet junction with a resistor model approach, its essential limitations stemming from inhomogeneous spin populations are clarified.
The democracy ochlocracy dictatorship transition in the Sznajd model and in the Ising model
Schneider, Johannes J.; Hirtreiter, Christian
2005-08-01
Since its introduction in 2000, the Sznajd model has been assumed to simulate a democratic community with two parties. The main flaw in this model is that a Sznajd system freezes in the long term in a non-democratic state, which can be either a dictatorship or a stalemate configuration. Here we show that the Sznajd model has better to be considered as a transition model, transferring a democratic system already at the beginning of a simulation via an ochlocratic scenario, i.e., a regime in which several mobs rule, to a dictatorship, thus reproducing the corresponding Aristotelian theory.
International Nuclear Information System (INIS)
Leite, R.V.; Oliveira Filho, L.O. de; Milton Pereira, J.; Cottam, M.G.; Costa Filho, R.N.
2009-01-01
A Green's function method is used to obtain the spectrum of spin excitations associated with a linear array of magnetic impurities implanted in a ferromagnetic thin film. The equations of motion for the Green's functions of the anisotropic film are written in the framework of the Ising model in a transverse field. The frequencies of localized modes are calculated as a function of the interaction parameters for the exchange coupling between impurity-spin pairs, host-spin pairs, and impurity-host neighbors, as well as the effective field parameter at the impurity sites.
Eising, G.; Kooi, B. J.
2012-01-01
Growth and decay of clusters at temperatures below T-c have been studied for a two-dimensional Ising model for both square and triangular lattices using Monte Carlo (MC) simulations and the enumeration of lattice animals. For the lattice animals, all unique cluster configurations with their internal
Kim, Eunhye; Lee, Sung Jong; Kim, Bongsoo
2007-02-01
We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density p through a dimer covering method. Building upon our recent work [Phys. Rev. E 68, 066127 (2003)] where we considered the nonequilibrium relaxation observed within the dominant sector with p=2/3, we here focus on the nonequilibrium kinetics within the minor sectors with psimple scaling behavior A(t)=A(t/tau(A)(p)), where the time scale tau(A)(p) shows a power-law divergence with vanishing p as tau(A)(p) approximately p(-phi) with phi approximately or equal to 4. These features can be understood in terms of random walk nature of the fluctuations of the strings within the typical separation between neighboring strings.
International Nuclear Information System (INIS)
Mariz, A.M.; Tsallis, C.; Albuquerque, E.L. de.
1984-01-01
The phae diagram for the Ising Model on a Cayley tree with competing nearest-neighbour interactions J 1 and next-nearest-neighbour interactions J 2 and J 3 in the presence of an external magnetic field is studied. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiro et al. At vanishing temperature, the phase diagram is fully determined, for all values and signs of J 2 /J 1 and J 3 /J 2 ; in particular, it is verified that values of J 3 /J 2 high enough favour the paramagnetic phase. At finite temperatures, several interesting features (evolution of re-entrances, separation of the modulated region in two disconnected pieces, etc.) are exhibited for typical values of J 2 /J 1 and J 3 /J 2 . (Author) [pt
International Nuclear Information System (INIS)
Kamieniarz, G.
1984-12-01
A zero temperature real space renormalization group block method is applied to the random quantum Ising model with a transverse field on the planar honeycomb and square lattices. For the bond diluted system the magnetisation and the separation of the ground state energy level (in the paramagnetic phase) are presented for several bond concentrations p. The critical exponents extracted both from the fixed-points and from direct numerical computations preserve some scaling relations, and the critical curve displays a characteristic discontinuity at the percolation concentration. For the McCoy and Wu distribution the random fields and bonds are found to introduce a strong relevant disorder. The order parameter still falls off continuously to zero for well-defined values of the parameters, but a new fixed point yields a slight change in the critical exponents. (author)
Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.
2018-05-01
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.
Quantum-memory-assisted entropic uncertainty in spin models with Dzyaloshinskii-Moriya interaction
Huang, Zhiming
2018-02-01
In this article, we investigate the dynamics and correlations of quantum-memory-assisted entropic uncertainty, the tightness of the uncertainty, entanglement, quantum correlation and mixedness for various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including the XXZ model with DM interaction, the XY model with DM interaction and the Ising model with DM interaction. We find that the uncertainty grows to a stable value with growing temperature but reduces as the coupling coefficient, anisotropy parameter and DM values increase. It is found that the entropic uncertainty is closely correlated with the mixedness of the system. The increasing quantum correlation can result in a decrease in the uncertainty, and the robustness of quantum correlation is better than entanglement since entanglement means sudden birth and death. The tightness of the uncertainty drops to zero, apart from slight volatility as various parameters increase. Furthermore, we propose an effective approach to steering the uncertainty by weak measurement reversal.
Schematic model of nuclear spin excitations
International Nuclear Information System (INIS)
Boucher, P.M.
1990-01-01
A simple model to estimate the strength of spin and nonspin collective states is presented. The model was inspired by early schematic models based on energy-weighted sum rules and is a useful tool for interpreting experimental data without the complexities of realistic microscopic calculations. The strength of collective states is calculated by assuming that a single collective state completely exhausts the energy-weighted sum rule. 19 refs
Distributed MAP in the SpinJa Model Checker
Directory of Open Access Journals (Sweden)
Stefan Vijzelaar
2011-10-01
Full Text Available Spin in Java (SpinJa is an explicit state model checker for the Promela modelling language also used by the SPIN model checker. Designed to be extensible and reusable, the implementation of SpinJa follows a layered approach in which each new layer extends the functionality of the previous one. While SpinJa has preliminary support for shared-memory model checking, it did not yet support distributed-memory model checking. This tool paper presents a distributed implementation of a maximal accepting predecessors (MAP search algorithm on top of SpinJa.
On spinfoam models in large spin regime
International Nuclear Information System (INIS)
Han, Muxin
2014-01-01
We study the semiclassical behavior of Lorentzian Engle–Pereira–Rovelli–Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so-called, almost analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as J f = λj f , where λ is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy γ Θ-ring f ≤λ −1/2 mod 4πZ. Our analysis results in a curvature expansion of the semiclassical low energy effective action from the spinfoam model, where the UV modifications of Einstein gravity appear as subleading high-curvature corrections. (paper)
International Nuclear Information System (INIS)
Mozeika, A; Coolen, A C C
2009-01-01
We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations
GPGPU Parallel SPIN Model Checker
National Aeronautics and Space Administration — Model Checking is a powerful technique used to verify that a system does not violate its intended behavior. While this is very useful in proving the robustness of a...
Mean field models for spin glasses
Talagrand, Michel
2011-01-01
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.
Parisi function for two spin glass models
International Nuclear Information System (INIS)
Sibani, P.; Hertz, J.A.
1984-01-01
The probability distribution function P(q) for the overlap of pairs of metastable states and the associated Parisi order function q(x) are calculated exactly at zero temperature for two simple models. The first is a chain in which each spin interacts randomly with the sum of all the spins between it and one end of the chain; the second is an infinite-range limit of a spin glass version of Dyson's hierarchical model. Both have nontrivial overlap distributions: In the first case the problem reduces to a variable-step-length random walk problem, leading to q(x)=sin(πx). In the second model P(q) can be calculated by a simple recursion relation which generates devil's staircase structure in q(x). If the fraction p of antiferromagnetic bonds is less than 1/√2, the staircase is complete and the fractal dimensionality of the complement of the domain where q(x) is flat is log 2/log (1/p 2 ). In both models the space of metastable states can be described in terms of Cayley trees, which however have a different physical interpretation than in the S.K. model. (orig.)
The dynamics of the Frustrated Ising Lattice Gas
International Nuclear Information System (INIS)
Arenzon, J.J.; Stariolo, D.A.; Ricci-Tersenghi, F.
2000-04-01
The dynamical properties of a three dimensional model glass, the Frustrated Ising Lattice Gas (FILG) are studied by Monte Carlo simulations. We present results of compression experiments, where the chemical potential is either slowly or abruptly changed, as well as simulations at constant density. One-time quantities like density and two-times ones as correlations, responses and mean square displacements are measured, and the departure from equilibrium clearly characterized. The aging scenario, particularly in the case of the density autocorrelations, is reminiscent of spin glass phenomenology with violations of the fluctuation-dissipation theorem, typical of systems with one replica symmetry breaking. The FILG, as a valid on-lattice model of structural glasses, can be described with tools developed in spin glass theory and, being a finite dimensional model, can open the way for a systematic study of activated processes in glasses. (author)
Ladder physics in the spin fermion model
Tsvelik, A. M.
2017-05-01
A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d -Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.
The Order Parameter in a Spin Glass
Enter, A.C.D. van; Griffiths, Robert B.
1983-01-01
Various possible precise definitions of an Edwards-Anderson type of order parameter for an Ising model spin glass are considered, using boundary conditions for a finite system, states of an infinite system, and a duplicate-system approach. Several of these definitions are shown to yield identical
Model independent spin determination at hadron colliders
International Nuclear Information System (INIS)
Edelhaeuser, Lisa
2012-01-01
By the end of the year 2011, both the CMS and ATLAS experiments at the Large Hadron Collider have recorded around 5 inverse femtobarns of data at an energy of 7 TeV. There are only vague hints from the already analysed data towards new physics at the TeV scale. However, one knows that around this scale, new physics should show up so that theoretical issues of the standard model of particle physics can be cured. During the last decades, extensions to the standard model that are supposed to solve its problems have been constructed, and the corresponding phenomenology has been worked out. As soon as new physics is discovered, one has to deal with the problem of determining the nature of the underlying model. A first hint is of course given by the mass spectrum and quantum numbers such as electric and colour charges of the new particles. However, there are two popular model classes, supersymmetric models and extradimensional models, which can exhibit almost equal properties at the accessible energy range. Both introduce partners to the standard model particles with the same charges and thus one needs an extended discrimination method. From the origin of these partners arises a relevant difference: The partners constructed in extradimensional models have the same spin as their standard model partners while in Supersymmetry they differ by spin 1/2. These different spins have an impact on the phenomenology of the two models. For example, one can exploit the fact that the total cross sections are affected, but this requires a very good knowledge of the couplings and masses involved. Another approach uses angular distributions depending on the particle spins. A prevailing method based on this idea uses the invariant mass distribution of the visible particles in decay chains. One can relate these distributions to the spin of the particle mediating the decay since it reflects itself in the highest power of the invariant mass s ff of the adjacent particles. In this thesis we
Model independent spin determination at hadron colliders
Energy Technology Data Exchange (ETDEWEB)
Edelhaeuser, Lisa
2012-04-25
By the end of the year 2011, both the CMS and ATLAS experiments at the Large Hadron Collider have recorded around 5 inverse femtobarns of data at an energy of 7 TeV. There are only vague hints from the already analysed data towards new physics at the TeV scale. However, one knows that around this scale, new physics should show up so that theoretical issues of the standard model of particle physics can be cured. During the last decades, extensions to the standard model that are supposed to solve its problems have been constructed, and the corresponding phenomenology has been worked out. As soon as new physics is discovered, one has to deal with the problem of determining the nature of the underlying model. A first hint is of course given by the mass spectrum and quantum numbers such as electric and colour charges of the new particles. However, there are two popular model classes, supersymmetric models and extradimensional models, which can exhibit almost equal properties at the accessible energy range. Both introduce partners to the standard model particles with the same charges and thus one needs an extended discrimination method. From the origin of these partners arises a relevant difference: The partners constructed in extradimensional models have the same spin as their standard model partners while in Supersymmetry they differ by spin 1/2. These different spins have an impact on the phenomenology of the two models. For example, one can exploit the fact that the total cross sections are affected, but this requires a very good knowledge of the couplings and masses involved. Another approach uses angular distributions depending on the particle spins. A prevailing method based on this idea uses the invariant mass distribution of the visible particles in decay chains. One can relate these distributions to the spin of the particle mediating the decay since it reflects itself in the highest power of the invariant mass s{sub ff} of the adjacent particles. In this thesis
Model independent spin determination at hadron colliders
Energy Technology Data Exchange (ETDEWEB)
Edelhaeuser, Lisa
2012-04-25
By the end of the year 2011, both the CMS and ATLAS experiments at the Large Hadron Collider have recorded around 5 inverse femtobarns of data at an energy of 7 TeV. There are only vague hints from the already analysed data towards new physics at the TeV scale. However, one knows that around this scale, new physics should show up so that theoretical issues of the standard model of particle physics can be cured. During the last decades, extensions to the standard model that are supposed to solve its problems have been constructed, and the corresponding phenomenology has been worked out. As soon as new physics is discovered, one has to deal with the problem of determining the nature of the underlying model. A first hint is of course given by the mass spectrum and quantum numbers such as electric and colour charges of the new particles. However, there are two popular model classes, supersymmetric models and extradimensional models, which can exhibit almost equal properties at the accessible energy range. Both introduce partners to the standard model particles with the same charges and thus one needs an extended discrimination method. From the origin of these partners arises a relevant difference: The partners constructed in extradimensional models have the same spin as their standard model partners while in Supersymmetry they differ by spin 1/2. These different spins have an impact on the phenomenology of the two models. For example, one can exploit the fact that the total cross sections are affected, but this requires a very good knowledge of the couplings and masses involved. Another approach uses angular distributions depending on the particle spins. A prevailing method based on this idea uses the invariant mass distribution of the visible particles in decay chains. One can relate these distributions to the spin of the particle mediating the decay since it reflects itself in the highest power of the invariant mass s{sub ff} of the adjacent particles. In this thesis
Nightingale, M.P.; Blöte, H.W.J.
1996-01-01
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity
Spin chain model for correlated quantum channels
Energy Technology Data Exchange (ETDEWEB)
Rossini, Davide [International School for Advanced Studies SISSA/ISAS, via Beirut 2-4, I-34014 Trieste (Italy); Giovannetti, Vittorio; Montangero, Simone [NEST-CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)], E-mail: monta@sns.it
2008-11-15
We analyze the quality of the quantum information transmission along a correlated quantum channel by studying the average fidelity between input and output states and the average output purity, giving bounds for the entropy of the channel. Noise correlations in the channel are modeled by the coupling of each channel use with an element of a one-dimensional interacting quantum spin chain. Criticality of the environment chain is seen to emerge in the changes of the fidelity and of the purity.
Quasi spin pairing and the structure of the Lipkin model
International Nuclear Information System (INIS)
Cambiaggio, M.C.; Plastino, A.
1978-01-01
By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A 'pairing plus monopole' model is studied in connection with the Hartree-Fock theory. (orig.) [de
Chakraborty, Saikat; Das, Subir K.
2017-09-01
Via Monte Carlo simulations we study pattern and aging during coarsening in a nonconserved nearest-neighbor Ising model, following quenches from infinite to zero temperature, in space dimension d = 3. The decay of the order-parameter autocorrelation function appears to obey a power-law behavior, as a function of the ratio between the observation and waiting times, in the large ratio limit. However, the exponent of the power law, estimated accurately via a state-of-the-art method, violates a well-known lower bound. This surprising fact has been discussed in connection with a quantitative picture of the structural anomaly that the 3D Ising model exhibits during coarsening at zero temperature. These results are compared with those for quenches to a temperature above that of the roughening transition.
Spin-flip dynamics of the Curie-Weiss model Loss of Gibbsianness with possibly broken symmetry.
Külske, C
2005-01-01
We study the conditional probabilities of the Curie-Weiss Ising model in vanishing external field under a symmetric independent stochastic spin-flip dynamics and discuss their set of bad configurations (points of discontinuity). We exhibit a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending the results for the corresponding lattice model, where only partial answers can be obtained. For initial inverse temperature $\\b \\leq 1$, we prove that the time-evolved measure is always Gibbsian. For $1 \\frac{3}{2}$, we observe the new phenomenon of symmetry-breaking of bad configurations: The time-evolved measure loses its Gibbsian character at a sharp transition time, and bad configurations with non-zero spin-average appear. These bad configurations merge into a neutral configuration at a later transition time, while the measure stays non-Gibbs. In our proof we give a detailed analysis of the phase-diagram of a Curie-Weiss random field Ising model with possi...
Thermodynamic curvature for a two-parameter spin model with frustration.
Ruppeiner, George; Bellucci, Stefano
2015-01-01
Microscopic models of realistic thermodynamic systems usually involve a number of parameters, not all of equal macroscopic relevance. We examine a decorated (1+3) Ising spin chain containing two microscopic parameters: a stiff parameter K mediating the long-range interactions, and a sloppy J operating within local spin groups. We show that K dominates the macroscopic behavior, with varying J having only a weak effect, except in regions where J brings about transitions between phases through its conditioning of the local spin groups with which K interacts. We calculate the heat capacity C(H), the magnetic susceptibility χ(T), and the thermodynamic curvature R. For large |J/K|, we identify four magnetic phases: ferromagnetic, antiferromagnetic, and two ferrimagnetic, according to the signs of K and J. We argue that for characterizing these phases, the strongest picture is offered by the thermodynamic geometric invariant R, proportional to the correlation length ξ. This picture has correspondences to other cases, such as fluids.
Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model
Paga, Pierre; Kühn, Reimer
2017-08-01
We study the large deviations of the magnetization at some finite time in the Curie-Weiss random field Ising model with parallel updating. While relaxation dynamics in an infinite-time horizon gives rise to unique dynamical trajectories [specified by initial conditions and governed by first-order dynamics of the form mt +1=f (mt) ] , we observe that the introduction of a finite-time horizon and the specification of terminal conditions can generate a host of metastable solutions obeying second-order dynamics. We show that these solutions are governed by a Newtonian-like dynamics in discrete time which permits solutions in terms of both the first-order relaxation ("forward") dynamics and the backward dynamics mt +1=f-1(mt) . Our approach allows us to classify trajectories for a given final magnetization as stable or metastable according to the value of the rate function associated with them. We find that in analogy to the Freidlin-Wentzell description of the stochastic dynamics of escape from metastable states, the dominant trajectories may switch between the two types (forward and backward) of first-order dynamics. Additionally, we show how to compute rate functions when uncertainty in the quenched disorder is introduced.
Simulation of multi-steps thermal transition in 2D spin-crossover nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Jureschi, Catalin-Maricel [LISV, Université de Versailles Saint-Quentin-en-Yvelines, 78140 Velizy (France); Faculty of Electrical Engineering and Computer Science and MANSiD, Stefan cel Mare University, Suceava 720229 (Romania); Pottier, Benjamin-Louis [Departement de Sciences Physiques, Université de Versailles Saint-Quentin-en-Yvelines, 78035 Versailles Cedex (France); Linares, Jorge, E-mail: jorge.linares@uvsq.fr [GEMaC, Université de Versailles Saint-Quentin-en-Yvelines, CNRS-UVSQ (UMR 8635), 78035 Versailles Cedex (France); Richard Dahoo, Pierre [LATMOS, Université de Versailles-Saint-Quentin-en-Yvelines, Sorbonne Universités, CNRS-UMR 8190, F-78280 Guyancourt (France); Alayli, Yasser [LISV, Université de Versailles Saint-Quentin-en-Yvelines, 78140 Velizy (France); Rotaru, Aurelian [Faculty of Electrical Engineering and Computer Science and MANSiD, Stefan cel Mare University, Suceava 720229 (Romania)
2016-04-01
We have used an Ising like model to study the thermal behavior of a 2D spin crossover (SCO) system embedded in a matrix. The interaction parameter between edge SCO molecules and its local environment was included in the standard Ising like model as an additional term. The influence of the system's size and the ratio between the number of edge molecules and the other molecules were also discussed.
The spin dependent odderon in the diquark model
Energy Technology Data Exchange (ETDEWEB)
Szymanowski, Lech [National Centre for Nuclear Research (NCBJ), Warsaw (Poland); Zhou, Jian, E-mail: jzhou@sdu.edu.cn [School of Physics, & Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Jinan, Shandong 250100 (China); Nikhef and Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, NL-1081 HV Amsterdam (Netherlands)
2016-09-10
In this short note, we report a di-quark model calculation for the spin dependent odderon and demonstrate that the asymmetrical color source distribution in the transverse plane of a transversely polarized hadron plays an essential role in yielding the spin dependent odderon. This calculation confirms the earlier finding that the spin dependent odderon is closely related to the parton orbital angular momentum.
DEFF Research Database (Denmark)
Larsen, J.; Schäffer, T. K.; Hansen, U. B.
2017-01-01
We present experimental evidence for a quantum phase transition in the easy-axis S = 3/2 anisotropic quasione-dimensional ferromagnet CoCl2 · 2D2O in a transverse field. Elastic neutron scattering shows that the magnetic order parameter vanishes at a transverse critical field μ0Hc = 16.05(4) T......, while inelastic neutron scattering shows that the gap in the magnetic excitation spectrum vanishes at the same field value, and reopens for H>Hc. The field dependence of the order parameter and the gap are well described by critical exponents β = 0.45 ± 0.09 and zν close to 1/2, implying...... that the quantum phase transition in CoCl2 · 2D2O differs significantly from the textbook version of a S = 1/2 Ising chain in a transverse field. We attribute the difference to weak but finite three-dimensionality of the magnetic interactions....
The spin-s quantum Heisenberg ferromagnetic models in the physical magnon theory
International Nuclear Information System (INIS)
Liu, B.-G.; Pu, F.-C.
2001-01-01
The spin-s quantum Heisenberg ferromagnetic model is investigated in the physical magnon theory. The effect of the extra unphysical magnon states on every site is completely removed in the magnon Hamiltonian and during approximation procedure so that the condition †n i a n i >=0(n≥2s+1) is rigorously satisfied. The physical multi-magnon occupancy †n i a n i >(1≤n≤2s) is proportional to T 3n/2 at low temperature and is equivalent to 1/(2s+1) at the Curie temperature. The magnetization not only unified but also well-behaved from zero temperature to Curie temperature is obtained in the framework of the magnon theory for the spin-s quantum Heisenberg ferromagnetic model. The ill-behaved magnetizations at high temperature in earlier magnon theories are completely corrected. The relation of magnon (spin wave) theory with spin-operator decoupling theory is clearly understood
Testing proton spin models with polarized beams
International Nuclear Information System (INIS)
Ramsey, G.P.
1991-01-01
We review models for spin-weighted parton distributions in a proton. Sum rules involving the nonsinglet components of the structure function xg 1 p help narrow the range of parameters in these models. The contribution of the γ 5 anomaly term depends on the size of the integrated polarized gluon distribution and experimental predictions depend on its size. We have proposed three models for the polarized gluon distributions, whose range is considerable. These model distributions give an overall range is considerable. These model distributions give an overall range of parameters that can be tested with polarized beam experiments. These are discussed with regard to specific predictions for polarized beam experiments at energies typical of UNK
Spin foam models for quantum gravity
International Nuclear Information System (INIS)
Perez, Alejandro
2003-01-01
In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett-Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett-Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants. (topical review)
Stochastic model of the spinning electron
International Nuclear Information System (INIS)
Simaciu, I.; Borsos, Z.
2002-01-01
In Stochastic Electrodynamics (SED) it is demonstrated that electrostatic interaction is the result of the scattering of the Classical Zero-Point Field (CZPF) background by the charged particles. In such models, the electron is modelled as a two-dimensional oscillator, which interacts with the electric component of the CZPF background. The electron with spin is not only an electric monopole but also a magnetic dipole. The interaction of the spin electron with the CZPF background is not only electric but also magnetic. We calculate the scattering cross-section of magnetic dipole in the situation when a magnetic field, variable in time B arrow = B 0 arrow sin ωt, acts over the rigid magnetic dipole given by the symmetry of the model. The cross-section of a magnetic dipole σ m must be equal to the cross-section of an electric monopole σ e . This equality between σ m and σ e cross-sections is motivated, too, by the fact that, in the model of the two-dimensional oscillator, the electric charge q e has the motion speed c. (authors)
International Nuclear Information System (INIS)
Scheinine, A.L.
1992-01-01
The frustrated XY model was studied on a lattice, primarily to test Fourier transform acceleration technique for a phase transition having more field structure than just spinwaves and vortices. Also, the spinless Hubbard model without hopping was simulated using continuous variables for the auxiliary field that mediates coupling between fermions. Finally, spin one-half Hubbard model was studied with a technique that sampled the fermion occupation configurations. The frustrated two-dimensional XY model was simulated using the Langevin equation with Fourier transform acceleration. Speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. The unfrustrated XY model was also studied. For the frustrated case, only long-distance spin correlation and the autocorrelation of the spin showed significant speedup. The frustrated case has Ising-like domains. It was found that Fourier acceleration speeds the evolution of spinwaves but has negligible effect on the Ising-like domains. In the Hubbard model, fermion determinant weight factor in the partition function changes sign, causing large statistical fluctuations of observables. A technique was found for sampling configuration space using continuous auxiliary fields, despite energy barriers where the fermion determinant changes sign. For two-dimensional spinless Hubbard model with no hopping, an exact solution was found for a 4 x 4 lattice; which could be compared to numerical simulations. The sign problem remained, and was found to be related to the sign problem encountered when a discrete variable is used for the auxiliary field. For spin one-half Hubbard model, a Monte Carlo simulation was done in which the fermion occupation configurations were varied. Rather than integrate-out the fermions and make a numerical estimate of the sum over the auxiliary field, the auxiliary field was integrated-out and a numerical estimate was made of the sum over fermion configurations
Frustrated lattices of Ising chains
International Nuclear Information System (INIS)
Kudasov, Yurii B; Korshunov, Aleksei S; Pavlov, V N; Maslov, Dmitrii A
2012-01-01
The magnetic structure and magnetization dynamics of systems of plane frustrated Ising chain lattices are reviewed for three groups of compounds: Ca 3 Co 2 O 6 , CsCoCl 3 , and Sr 5 Rh 4 O 12 . The available experimental data are analyzed and compared in detail. It is shown that a high-temperature magnetic phase on a triangle lattice is normally and universally a partially disordered antiferromagnetic (PDA) structure. The diversity of low-temperature phases results from weak interactions that lift the degeneracy of a 2D antiferromagnetic Ising model on the triangle lattice. Mean-field models, Monte Carlo simulation results on the static magnetization curve, and results on slow magnetization dynamics obtained with Glauber's theory are discussed in detail. (reviews of topical problems)
A comparison of portfolio selection models via application on ISE 100 index data
Altun, Emrah; Tatlidil, Hüseyin
2013-10-01
Markowitz Model, a classical approach to portfolio optimization problem, relies on two important assumptions: the expected return is multivariate normally distributed and the investor is risk averter. But this model has not been extensively used in finance. Empirical results show that it is very hard to solve large scale portfolio optimization problems with Mean-Variance (M-V)model. Alternative model, Mean Absolute Deviation (MAD) model which is proposed by Konno and Yamazaki [7] has been used to remove most of difficulties of Markowitz Mean-Variance model. MAD model don't need to assume that the probability of the rates of return is normally distributed and based on Linear Programming. Another alternative portfolio model is Mean-Lower Semi Absolute Deviation (M-LSAD), which is proposed by Speranza [3]. We will compare these models to determine which model gives more appropriate solution to investors.
Ladder physics in the spin fermion model
International Nuclear Information System (INIS)
Tsvelik, A. M.
2017-01-01
A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. Here, it is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.
Low spin models for higher-spin Lagrangians
Czech Academy of Sciences Publication Activity Database
Francia, Dario
2011-01-01
Roč. 2011, č. 188 (2011), s. 94-105 ISSN 0375-9687. [International Conference on String Field Theory and Related Aspects (SFT2010). Kyoto, 18.10.2010-22.10.2010] Grant - others:EUROHORC and ESF(XE) EYI/07/E010 Institutional research plan: CEZ:AV0Z10100502 Keywords : higher spin theories * Maxwell's equations * open string theory Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 1.063, year: 2011 http://ptp.ipap.jp/link?PTPS/188/94/
A low-temperature derivation of spin-spin exchange in Kondo lattice model
International Nuclear Information System (INIS)
Feng Szeshiang; Mochena, Mogus
2005-01-01
Using Hubbard-Stratonovich transformation and drone-fermion representations for spin-12 and for spin-32, which is presented for the first time, we make a path-integral formulation of the Kondo lattice model. In the case of weak coupling and low temperature, the functional integral over conduction fermions can be approximated to the quadratic order and this gives the well-known RKKY interaction. In the case of strong coupling, the same quadratic approximation leads to an effective local spin-spin interaction linear in hopping energy t
A low-temperature derivation of spin-spin exchange in Kondo lattice model
Energy Technology Data Exchange (ETDEWEB)
Feng Szeshiang [Physics Department, Florida A and M University, Tallahassee, FL 32307 (United States)]. E-mail: shixiang.feng@famu.edu; Mochena, Mogus [Physics Department, Florida A and M University, Tallahassee, FL 32307 (United States)
2005-11-01
Using Hubbard-Stratonovich transformation and drone-fermion representations for spin-12 and for spin-32, which is presented for the first time, we make a path-integral formulation of the Kondo lattice model. In the case of weak coupling and low temperature, the functional integral over conduction fermions can be approximated to the quadratic order and this gives the well-known RKKY interaction. In the case of strong coupling, the same quadratic approximation leads to an effective local spin-spin interaction linear in hopping energy t.
Theory of spin Hall effect: extension of the Drude model.
Chudnovsky, Eugene M
2007-11-16
An extension of the Drude model is proposed that accounts for the spin and spin-orbit interaction of charge carriers. Spin currents appear due to the combined action of the external electric field, crystal field, and scattering of charge carriers. The expression for the spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, the spin Hall conductivity sigma s and charge conductivity sigma c are related through sigma s=[2pi variant /(3mc2)]sigma2c with m being the bare electron mass. The theoretically computed value is in agreement with experiment.
Critical properties of a simple spin glass model
International Nuclear Information System (INIS)
Aharony, A.; Imry, Y.
1976-01-01
The Mattis spin glass model is described as following from a particular quenched random solid solution picture, and its zero-field properties are discussed. The random field model is reviewed. The application to the spin glass problem is made and the more general scaling theory presented, and the limitations of the model are discussed
Exposure Modeling Tools and Databases for Consideration for Relevance to the Amended TSCA (ISES)
The Agency’s Office of Research and Development (ORD) has a number of ongoing exposure modeling tools and databases. These efforts are anticipated to be useful in supporting ongoing implementation of the amended Toxic Substances Control Act (TSCA). Under ORD’s Chemic...
Ising-based model of opinion formation in a complex network of interpersonal interactions
Grabowski, A.; Kosiński, R. A.
2006-03-01
In our work the process of opinion formation in the human population, treated as a scale-free network, is modeled and investigated numerically. The individuals (nodes of the network) are characterized by their authorities, which influence the interpersonal interactions in the population. Hierarchical, two-level structures of interpersonal interactions and spatial localization of individuals are taken into account. The effect of the mass media, modeled as an external stimulation acting on the social network, on the process of opinion formation is investigated. It was found that in the time evolution of opinions of individuals critical phenomena occur. The first one is observed in the critical temperature of the system TC and is connected with the situation in the community, which may be described by such quantifiers as the economic status of people, unemployment or crime wave. Another critical phenomenon is connected with the influence of mass media on the population. As results from our computations, under certain circumstances the mass media can provoke critical rebuilding of opinions in the population.
Annealed n-vector p spin model
International Nuclear Information System (INIS)
Taucher, T.; Frankel, N.E.
1992-01-01
A disordered n-vector model with p spin interactions is introduced and studied in mean field theory for the annealed case. The complete solutions for the cases n = 2 and n = 3, is presented and explicit order parameter equations is given for all the stable solutions for arbitrary n. For all n and p was found on stable high temperature phase and one stable low temperature phase. The phase transition is of first order. For n = 2, it is continuous in the order parameters for p ≤ 4 and has a jump discontinuity in the order parameters if p > 4. For n = 3, it has a jump discontinuity in the order parameters for all p. 11 refs., 4 figs
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
temperature are studied as functions of temperature, time, and concentration. At zero temperature and high dilution, the growing solid is found to have a fractal morphology and the effective fractal exponent D varies with concentration and ratio of time scales of the two dynamical processes. The mechanism...... responsible for forming the fractal solid is shown to be a buildup of a locally high vacancy concentration in the active growth zone. The growth-probability measure of the fractals is analyzed in terms of multifractality by calculating the f(α) spectrum. It is shown that the basic ideas of relating...... probability measures of static fractal objects to the growth-probability distribution during formation of the fractal apply to the present model. The f(α) spectrum is found to be in the universality class of diffusion-limited aggregation. At finite temperatures, the fractal solid domains become metastable...
The effect of spin in swing bowling in cricket: model trajectories for spin alone
Robinson, Garry; Robinson, Ian
2015-02-01
In ‘swing’ bowling, as employed by fast and fast-medium bowlers in cricket, back-spin along the line of the seam is normally applied in order to keep the seam vertical and to provide stability against ‘wobble’ of the seam. Whilst spin is normally thought of as primarily being the slow bowler's domain, the spin applied by the swing bowler has the side-effect of generating a lift or Magnus force. This force, depending on the orientation of the seam and hence that of the back-spin, can have a side-ways component as well as the expected vertical ‘lift’ component. The effect of the spin itself, in influencing the trajectory of the fast bowler's delivery, is normally not considered, presumably being thought of as negligible. The purpose of this paper is to investigate, using calculated model trajectories, the amount of side-ways movement due to the spin and to see how this predicted movement compares with the total observed side-ways movement. The size of the vertical lift component is also estimated. It is found that, although the spin is an essential part of the successful swing bowler's delivery, the amount of side-ways movement due to the spin itself amounts to a few centimetres or so, and is therefore small, but perhaps not negligible, compared to the total amount of side-ways movement observed. The spin does, however, provide a considerable amount of lift compared to the equivalent delivery bowled without spin, altering the point of pitching by up to 3 m, a very large amount indeed. Thus, for example, bowling a ball with the seam pointing directly down the pitch and not designed to swing side-ways at all, but with the amount of back-spin varied, could provide a very powerful additional weapon in the fast bowler's arsenal. So-called ‘sling bowlers’, who use a very low arm action, can take advantage of spin since effectively they can apply side-spin to the ball, giving rise to a large side-ways movement, ˜ 20{}^\\circ cm or more, which certainly is
Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet
Wauters, Matteo M.; Fazio, Rosario; Nishimori, Hidetoshi; Santoro, Giuseppe E.
2017-08-01
We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the p -spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second order (p =2 , the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition (p ≥3 , i.e., with multispin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards zero when the total annealing time τ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a nonequilibrium Landau-Zener analysis. We also analyze the imaginary-time QA dynamics of the model, finding a 1 /τ2 behavior for all finite values of p , as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit p (odd )=∞ is also discussed.
Spherical 2+p spin-glass model: An exactly solvable model for glass to spin-glass transition
International Nuclear Information System (INIS)
Crisanti, A.; Leuzzi, L.
2004-01-01
We present the full phase diagram of the spherical 2+p spin-glass model with p≥4. The main outcome is the presence of a phase with both properties of full replica symmetry breaking phases of discrete models, e.g., the Sherrington-Kirkpatrick model, and those of one replica symmetry breaking. This phase has a finite complexity which leads to different dynamic and static properties. The phase diagram is rich enough to allow the study of different kinds of glass to spin glass and spin glass to spin glass phase transitions
(Non-) Gibbsianness and Phase Transitions in Random Lattice Spin Models
Külske, C.
1999-01-01
We consider disordered lattice spin models with finite-volume Gibbs measures µΛ[η](dσ). Here σ denotes a lattice spin variable and η a lattice random variable with product distribution P describing the quenched disorder of the model. We ask: when will the joint measures limΛ↑Zd P(dη)µΛ[η](dσ) be
STOCHASTIC MODEL OF THE SPIN DISTRIBUTION OF DARK MATTER HALOS
Energy Technology Data Exchange (ETDEWEB)
Kim, Juhan [Center for Advanced Computation, Korea Institute for Advanced Study, Heogiro 85, Seoul 130-722 (Korea, Republic of); Choi, Yun-Young [Department of Astronomy and Space Science, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of); Kim, Sungsoo S.; Lee, Jeong-Eun [School of Space Research, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of)
2015-09-15
We employ a stochastic approach to probing the origin of the log-normal distributions of halo spin in N-body simulations. After analyzing spin evolution in halo merging trees, it was found that a spin change can be characterized by a stochastic random walk of angular momentum. Also, spin distributions generated by random walks are fairly consistent with those directly obtained from N-body simulations. We derived a stochastic differential equation from a widely used spin definition and measured the probability distributions of the derived angular momentum change from a massive set of halo merging trees. The roles of major merging and accretion are also statistically analyzed in evolving spin distributions. Several factors (local environment, halo mass, merging mass ratio, and redshift) are found to influence the angular momentum change. The spin distributions generated in the mean-field or void regions tend to shift slightly to a higher spin value compared with simulated spin distributions, which seems to be caused by the correlated random walks. We verified the assumption of randomness in the angular momentum change observed in the N-body simulation and detected several degrees of correlation between walks, which may provide a clue for the discrepancies between the simulated and generated spin distributions in the voids. However, the generated spin distributions in the group and cluster regions successfully match the simulated spin distribution. We also demonstrated that the log-normality of the spin distribution is a natural consequence of the stochastic differential equation of the halo spin, which is well described by the Geometric Brownian Motion model.
Random field Ising chain and neutral networks with synchronous dynamics
International Nuclear Information System (INIS)
Skantzos, N.S.; Coolen, A.C.C.
2001-01-01
We first present an exact solution of the one-dimensional random-field Ising model in which spin-updates are made fully synchronously, i.e. in parallel (in contrast to the more conventional Glauber-type sequential rules). We find transitions where the support of local observables turns from a continuous interval into a Cantor set and we show that synchronous and sequential random-field models lead asymptotically to the same physical states. We then proceed to an application of these techniques to recurrent neural networks where 1D short-range interactions are combined with infinite-range ones. Due to the competing interactions these models exhibit phase diagrams with first-order transitions and regions with multiple locally stable solutions for the macroscopic order parameters
Compiling gate networks on an Ising quantum computer
International Nuclear Information System (INIS)
Bowdrey, M.D.; Jones, J.A.; Knill, E.; Laflamme, R.
2005-01-01
Here we describe a simple mechanical procedure for compiling a quantum gate network into the natural gates (pulses and delays) for an Ising quantum computer. The aim is not necessarily to generate the most efficient pulse sequence, but rather to develop an efficient compilation algorithm that can be easily implemented in large spin systems. The key observation is that it is not always necessary to refocus all the undesired couplings in a spin system. Instead, the coupling evolution can simply be tracked and then corrected at some later time. Although described within the language of NMR, the algorithm is applicable to any design of quantum computer based on Ising couplings
Analysis of multi-step transitions in spin crossover nanochains
Energy Technology Data Exchange (ETDEWEB)
Chiruta, Daniel [GEMaC, Université de Versailles Saint-Quentin-en-Yvelines, CNRS-UVSQ (UMR 8635), 78035 Versailles Cedex (France); LISV, Université de Versailles Saint-Quentin-en-Yvelines, 78140 Velizy (France); Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University, Suceava 720229 (Romania); Linares, Jorge, E-mail: jorge.linares@uvsq.fr [GEMaC, Université de Versailles Saint-Quentin-en-Yvelines, CNRS-UVSQ (UMR 8635), 78035 Versailles Cedex (France); Garcia, Yann, E-mail: yann.garcia@uclouvain.be [Institute of Condensed Matter and Nanosciences, Université Catholique de Louvain, Molecules, Solids and Reactivity (IMCN/MOST), Place Louis Pasteur, 1, 1348 Louvain-la-Neuve (Belgium); Dimian, Mihai [Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University, Suceava 720229 (Romania); Dahoo, Pierre Richard [LATMOS, Université de Versailles-Saint-Quentin-en-Yvelines, CNRS-UPMC-UVSQ (UMR 8190), 78280 Guyancourt (France)
2014-02-01
The temperature driven phase transition occurring in spin crossover nanochains has been studied by an Ising-like model considering both short-range and long-range interactions. Various types of spin crossover profiles have been described in this framework, including a novel three-step transition identified in a nanosystem with eight molecules, which is modeled for the first time. A special interest has been also given to stepwise transitions accompanied by two hysteresis loops. The edge and size effects on spin crossover behavior have been investigated in order to get a deeper insight of the underlying mechanisms involved in these unusual spin transitions.
Giant magnetocaloric effect, magnetization plateaux and jumps of the regular Ising polyhedra
International Nuclear Information System (INIS)
Strečka, Jozef; Karľová, Katarína; Madaras, Tomáš
2015-01-01
Magnetization process and adiabatic demagnetization of the antiferromagnetic Ising spin clusters with the shape of regular polyhedra (Platonic solids) are exactly examined within the framework of a simple graph-theoretical approach. While the Ising cube as the only unfrustrated (bipartite) spin cluster shows just one trivial plateau at zero magnetization, the other regular Ising polyhedra (tetrahedron, octahedron, icosahedron and dodecahedron) additionally display either one or two intermediate plateaux at fractional values of the saturation magnetization. The nature of highly degenerate ground states emergent at intermediate plateaux owing to a geometric frustration is clarified. It is evidenced that the regular Ising polyhedra exhibit a giant magnetocaloric effect in a vicinity of magnetization jumps, whereas the Ising octahedron and dodecahedron belong to the most prominent geometrically frustrated spin clusters that enable an efficient low-temperature refrigeration by the process of adiabatic demagnetization
Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics
Franjo, FRANJIC; Sandro, SORELLA; Istituto Nazionale di Fisica della Materia International School for Advance Studies; Istituto Nazionale di Fisica della Materia International School for Advance Studies
1997-01-01
We present a new approach to determine an accurate variational wave function for general quantum spin models, completely defined by a consistency requirement with the simple and well-known linear spin-wave expansion. With this wave function, it is also possible to obtain the correct behavior of the long distance correlation functions for the 1D S=1/2 antiferromagnet. In 2D the proposed spin-wave wave function represents an excellent approximation to the exact ground state of the S=1.2 XY mode...
Tunnel splitting in biaxial spin models investigated with spin-coherent-state path integrals
International Nuclear Information System (INIS)
Chen Zhide; Liang, J.-Q.; Pu, F.-C.
2003-01-01
Tunnel splitting in biaxial spin models is investigated with a full evaluation of the fluctuation functional integrals of the Euclidean kernel in the framework of spin-coherent-state path integrals which leads to a magnitude of tunnel splitting quantitatively comparable with the numerical results in terms of diagonalization of the Hamilton operator. An additional factor resulted from a global time transformation converting the position-dependent mass to a constant one seems to be equivalent to the semiclassical correction of the Lagrangian proposed by Enz and Schilling. A long standing question whether the spin-coherent-state representation of path integrals can result in an accurate tunnel splitting is therefore resolved
Phi4 lattice field theory as an asymptotic expansion about the Ising limit
International Nuclear Information System (INIS)
Caginalp, G.
1980-01-01
For a d-dimensional phi 4 lattice field theory consisting of N spins, an asymptotic expansion of expectations about the Ising limit is established in inverse powers of the bare coupling constant lambda. In the thermodynamic limit (N→infinity), the expansion is expected to be valid in the noncritical region of the Ising system
Minimal model of spin-transfer torque and spin pumping caused by the spin Hall Effect
Czech Academy of Sciences Publication Activity Database
Chen, W.; Sigrist, M.; Sinova, Jairo; Manske, D.
2016-01-01
Roč. 115, č. 21 (2016), 1-5, č. článku 217203. ISSN 0031-9007 Institutional support: RVO:68378271 Keywords : spintronics * spin Hall effect Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 8.462, year: 2016
Kinetic models in spin chemistry. 1. The hyperfine interaction
DEFF Research Database (Denmark)
Mojaza, M.; Pedersen, J. B.
2012-01-01
Kinetic models for quantum systems are quite popular due to their simplicity, although they are difficult to justify. We show that the transformation from quantum to kinetic description can be done exactly for the hyperfine interaction of one nuclei with arbitrary spin; more spins are described w...... induced enhancement of the reaction yield. (C) 2012 Elsevier B.V. All rights reserved....
The proton's spin: A quark model perspective
International Nuclear Information System (INIS)
Close, F.E.
1989-01-01
Magnetic moments and g A /g V provide information on the correlations among quark spins and flavors in the proton. I compare this information with the deep inelastic polarized data from EMC which has been claimed to show that very little of the proton's spin is due to the quarks. The possibility that there is significant polarization of strange quarks within protons is discussed. 38 refs
Pressure and Temperature Sensors Using Two Spin Crossover Materials.
Jureschi, Catalin-Maricel; Linares, Jorge; Boulmaali, Ayoub; Dahoo, Pierre Richard; Rotaru, Aurelian; Garcia, Yann
2016-02-02
The possibility of a new design concept for dual spin crossover based sensors for concomitant detection of both temperature and pressure is presented. It is conjectured from numerical results obtained by mean field approximation applied to a Ising-like model that using two different spin crossover compounds containing switching molecules with weak elastic interactions it is possible to simultaneously measure P and T. When the interaction parameters are optimized, the spin transition is gradual and for each spin crossover compounds, both temperature and pressure values being identified from their optical densities. This concept offers great perspectives for smart sensing devices.
Pressure and Temperature Sensors Using Two Spin Crossover Materials
Jureschi, Catalin-Maricel; Linares, Jorge; Boulmaali, Ayoub; Dahoo, Pierre Richard; Rotaru, Aurelian; Garcia, Yann
2016-01-01
The possibility of a new design concept for dual spin crossover based sensors for concomitant detection of both temperature and pressure is presented. It is conjectured from numerical results obtained by mean field approximation applied to a Ising-like model that using two different spin crossover compounds containing switching molecules with weak elastic interactions it is possible to simultaneously measure P and T. When the interaction parameters are optimized, the spin transition is gradual and for each spin crossover compounds, both temperature and pressure values being identified from their optical densities. This concept offers great perspectives for smart sensing devices. PMID:26848663
Pressure and Temperature Sensors Using Two Spin Crossover Materials
Directory of Open Access Journals (Sweden)
Catalin-Maricel Jureschi
2016-02-01
Full Text Available The possibility of a new design concept for dual spin crossover based sensors for concomitant detection of both temperature and pressure is presented. It is conjectured from numerical results obtained by mean field approximation applied to a Ising-like model that using two different spin crossover compounds containing switching molecules with weak elastic interactions it is possible to simultaneously measure P and T. When the interaction parameters are optimized, the spin transition is gradual and for each spin crossover compounds, both temperature and pressure values being identified from their optical densities. This concept offers great perspectives for smart sensing devices.
Conformal bootstrap with slightly broken higher spin symmetry
Energy Technology Data Exchange (ETDEWEB)
Alday, Luis F. [Mathematical Institute, University of Oxford,Andrew Wiles Building, Radcliffe Observatory Quarter,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Zhiboedov, Alexander [Center for the Fundamental Laws of Nature,Harvard University, Cambridge, MA 02138 (United States)
2016-06-16
We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents γ{sub s} with large spin s. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.
International Nuclear Information System (INIS)
Li Jun; Wei Guozhu; Du An
2005-01-01
The compensation and critical behaviors of a mixed spin-2 and spin-12 Heisenberg ferrimagnetic system on a square lattice are investigated theoretically by the two-time Green's function technique, which takes into account the quantum nature of Heisenberg spins. The model can be relevant for understanding the magnetic behavior of the new class of organometallic ferromagnetic materials that exhibit spontaneous magnetic properties at room temperature. We carry out the calculation of the sublattice magnetizations and the spin-wave spectra of the ground state. In particular, we have studied the effects of the nearest, next-nearest-neighbor interactions, the crystal field and the external magnetic field on the compensation temperature and the critical temperature. When only the nearest-neighbor interactions and the crystal field are included, no compensation temperature exists; when the next-nearest-neighbor interaction between spin-12 is taken into account and exceeds a minimum value, a compensation point appears and it is basically unchanged for other parameters in Hamiltonian fixed. The next-nearest-neighbor interactions between spin-2 and the external magnetic field have the effects of changing the compensation temperature and there is a narrow range of parameters of the Hamiltonian for which the model has the compensation temperatures and compensation temperature exists only for a small value of them
Stimulated polarization wave process in spin 3/2 chains
International Nuclear Information System (INIS)
Furman, G. B.
2007-01-01
Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Recently, it has been demonstrated that, in an idealized one-dimensional Ising spin 1/2 chain with nearest-neighbor interactions and realistic spin 1/2 chain including the natural dipole-dipole interactions, irradiated by a weak resonant transverse field, a wave of flipped spins can be triggered by a single spin flip. Here we focuse on control of polarization wave in chain of spin 3/2, where the nuclear quadrupole interaction is dominant. Results of simulations for 1D spin chains and rings with up to five spins are presented.
International Nuclear Information System (INIS)
Bhattacherjee, Aranya B; Jha, Pradip; Kumar, Tarun; Mohan, Man
2011-01-01
We study the physical properties of a Luttinger liquid in a superlattice that is characterized by alternating two tunneling parameters. Using the bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonaga-Luttinger model. We analyze the spin-charge separation and transport properties of the superlattice system. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We find that the classical two-point correlator decreases as the difference between the two tunneling parameters increases.
Ising ferromagnet: zero-temperature dynamic evolution
International Nuclear Information System (INIS)
Oliveira, P M C de; Newman, C M; Sidoravicious, V; Stein, D L
2006-01-01
The dynamic evolution at zero temperature of a uniform Ising ferromagnet on a square lattice is followed by Monte Carlo computer simulations. The system always eventually reaches a final, absorbing state, which sometimes coincides with a ground state (all spins parallel), and sometimes does not (parallel stripes of spins up and down). We initiate here the numerical study of 'chaotic time dependence' (CTD) by seeing how much information about the final state is predictable from the randomly generated quenched initial state. CTD was originally proposed to explain how nonequilibrium spin glasses could manifest an equilibrium pure state structure, but in simpler systems such as homogeneous ferromagnets it is closely related to long-term predictability and our results suggest that CTD might indeed occur in the infinite volume limit
Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network
International Nuclear Information System (INIS)
Surungan, Tasrief; Zen, Freddy P; Williams, Anthony G
2015-01-01
Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in d-dimensional regular lattices for (d ≤ 3). We can make an analogy for the connectivity density (m) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of m for the existence of SG behaviour, analogous to the lower critical dimension (d l ) for the canonical SG systems. Here we study system with m = 2, 3, 4 and 5. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of m and estimated its corersponding critical temperature. (paper)
Ground state properties of a spin chain within Heisenberg model with a single lacking spin site
International Nuclear Information System (INIS)
Mebrouki, M.
2011-01-01
The ground state and first excited state energies of an antiferromagnetic spin-1/2 chain with and without a single lacking spin site are computed using exact diagonalization method, within the Heisenberg model. In order to keep both parts of a spin chain with a lacking site connected, next nearest neighbors interactions are then introduced. Also, the Density Matrix Renormalization Group (DMRG) method is used, to investigate ground state energies of large system sizes; which permits us to inquire about the effect of large system sizes on energies. Other quantum quantities such as fidelity and correlation functions are also studied and compared in both cases. - Research highlights: → In this paper we compute ground state and first excited state energies of a spin chain with and without a lacking spin site. The next nearest neighbors are introduced with the antiferromagnetic Heisenberg spin-half. → Exact diagonalization is used for small systems, where DMRG method is used to compute energies for large systems. Other quantities like quantum fidelity and correlation are also computed. → Results are presented in figures with comments. → E 0 /N is computed in a function of N for several values of J 2 and for both systems. First excited energies are also investigated.
Out-of-time-ordered correlators in a quantum Ising chain
Lin, Cheng-Ju; Motrunich, Olexei I.
2018-04-01
Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a "shell-like" structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t-1 power law at long time t . On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like" structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t-1 /4 for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a "ball-like" structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.
International Nuclear Information System (INIS)
Dalmazi, D; Sa, F L
2010-01-01
Here we study the partition function zeros of the one-dimensional Blume-Emery-Griffiths model close to their edge singularities. The model contains four couplings (H, J, Δ, K) including the magnetic field H and the Ising coupling J. We assume that only one of the three couplings (J, Δ, K) is complex and the magnetic field is real. The generalized zeros z i tend to form continuous curves on the complex z-plane in the thermodynamic limit. The linear density at the edges z E diverges usually with ρ(z) ∼ |z - z E | σ and σ = -1/2. However, as in the case of complex magnetic fields (Yang-Lee edge singularity), if we have a triple degeneracy of the transfer matrix eigenvalues a new critical behavior with σ = -2/3 can appear as we prove here explicitly for the cases where either Δ or K is complex. Our proof applies for a general three-state spin model with short-range interactions. The Fisher zeros (complex J) are more involved; in practice, we have not been able to find an explicit example with σ = -2/3 as far as the other couplings (H, Δ, K) are kept as real numbers. Our results are supported by numerical computations of zeros. We show that it is absolutely necessary to have a non-vanishing magnetic field for a new critical behavior. The appearance of σ = -2/3 at the edge closest to the positive real axis indicates its possible relevance for tricritical phenomena in higher-dimensional spin models.
Herding, minority game, market clearing and efficient markets in a simple spin model framework
Kristoufek, Ladislav; Vosvrda, Miloslav
2018-01-01
We present a novel approach towards the financial Ising model. Most studies utilize the model to find settings which generate returns closely mimicking the financial stylized facts such as fat tails, volatility clustering and persistence, and others. We tackle the model utility from the other side and look for the combination of parameters which yields return dynamics of the efficient market in the view of the efficient market hypothesis. Working with the Ising model, we are able to present nicely interpretable results as the model is based on only two parameters. Apart from showing the results of our simulation study, we offer a new interpretation of the Ising model parameters via inverse temperature and entropy. We show that in fact market frictions (to a certain level) and herding behavior of the market participants do not go against market efficiency but what is more, they are needed for the markets to be efficient.
Non-Abelian anyons: when Ising meets Fibonacci
Grosfeld, E.; Schoutens, K.
2009-01-01
We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting Ising anyons, and the k=2 non-Abelian spin-singlet state, supporting Fibonacci anyons. It is shown that the interface supports neutral excitations described by a (1+1)-dimensional conformal field
Ground states of a spin-boson model
International Nuclear Information System (INIS)
Amann, A.
1991-01-01
Phase transition with respect to ground states of a spin-boson Hamiltonian are investigated. The spin-boson model under discussion consists of one spin and infinitely many bosons with a dipole-type coupling. It is shown that the order parameter of the model vanishes with respect to arbitrary ground states if it vanishes with respect to ground states obtained as (biased) temperature to zero limits of thermic equilibrium states. The ground states of the latter special type have been investigated by H. Spohn. Spohn's respective phase diagrams are therefore valid for arbitrary ground states. Furthermore, disjointness of ground states in the broken symmetry regime is examined
Network of time-multiplexed optical parametric oscillators as a coherent Ising machine
Marandi, Alireza; Wang, Zhe; Takata, Kenta; Byer, Robert L.; Yamamoto, Yoshihisa
2014-12-01
Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.
Analytic Models for Sunlight Charging of a Rapidly Spinning Satellite
National Research Council Canada - National Science Library
Tautz, Maurice
2003-01-01
... photoelectrons can be blocked by local potential barriers. In this report, we discuss two analytic models for sunlight charging of a rapidly spinning spherical satellite, both of which are based on blocked photoelectron currents...
International Nuclear Information System (INIS)
Nam, Keekwon; Kim, Bongsoo; Park, Sangwoong; Lee, Sung Jong
2011-01-01
We present a numerical study on an interacting monomer–dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the Z 2 symmetry-breaking order–disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even within the absorbing phase. Our findings call for further studies on microscopic models and the corresponding continuum description belonging to the generalized voter university class. (letter)
Magnetic and electric order in the spin-1/2 XX model with three-spin interactions
Energy Technology Data Exchange (ETDEWEB)
Thakur, Pradeep; Durganandini, P. [Department of Physics, University of Pune, Ganeshkhind, Pune - 411007 (India)
2016-05-23
We study the spin-1/2 XX model in the presence of three-spin interactions of the XZX+YZY and XZY-YZX types. We solve the problem exactly and show that there is both finite magnetization and electric polarization for low non-zero strengths of the three-spin interactions.
Spin Glass Models of Syntax and Language Evolution
Siva, Karthik; Tao, Jim; Marcolli, Matilde
2015-01-01
Using the SSWL database of syntactic parameters of world languages, and the MIT Media Lab data on language interactions, we construct a spin glass model of language evolution. We treat binary syntactic parameters as spin states, with languages as vertices of a graph, and assigned interaction energies along the edges. We study a rough model of syntax evolution, under the assumption that a strong interaction energy tends to cause parameters to align, as in the case of ferromagnetic materials. W...
Continuum model for chiral induced spin selectivity in helical molecules
Energy Technology Data Exchange (ETDEWEB)
Medina, Ernesto [Centro de Física, Instituto Venezolano de Investigaciones Científicas, 21827, Caracas 1020 A (Venezuela, Bolivarian Republic of); Groupe de Physique Statistique, Institut Jean Lamour, Université de Lorraine, 54506 Vandoeuvre-les-Nancy Cedex (France); Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287 (United States); González-Arraga, Luis A. [IMDEA Nanoscience, Cantoblanco, 28049 Madrid (Spain); Finkelstein-Shapiro, Daniel; Mujica, Vladimiro [Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287 (United States); Berche, Bertrand [Centro de Física, Instituto Venezolano de Investigaciones Científicas, 21827, Caracas 1020 A (Venezuela, Bolivarian Republic of); Groupe de Physique Statistique, Institut Jean Lamour, Université de Lorraine, 54506 Vandoeuvre-les-Nancy Cedex (France)
2015-05-21
A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented p{sub z} type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the spin-orbit coupling (SOC) opens up an effective π{sub z} − π{sub z} coupling via interbase p{sub x,y} − p{sub z} hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry; nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts (i) which spin orientation is selected depending on chirality and bias, (ii) changes in spin preference as a function of input Fermi level and (iii) back-scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov-Anandan phase. To describe room temperature transport, we assume that the total transmission is the result of a product of coherent steps.
Vector spin modeling for magnetic tunnel junctions with voltage dependent effects
International Nuclear Information System (INIS)
Manipatruni, Sasikanth; Nikonov, Dmitri E.; Young, Ian A.
2014-01-01
Integration and co-design of CMOS and spin transfer devices requires accurate vector spin conduction modeling of magnetic tunnel junction (MTJ) devices. A physically realistic model of the MTJ should comprehend the spin torque dynamics of nanomagnet interacting with an injected vector spin current and the voltage dependent spin torque. Vector spin modeling allows for calculation of 3 component spin currents and potentials along with the charge currents/potentials in non-collinear magnetic systems. Here, we show 4-component vector spin conduction modeling of magnetic tunnel junction devices coupled with spin transfer torque in the nanomagnet. Nanomagnet dynamics, voltage dependent spin transport, and thermal noise are comprehended in a self-consistent fashion. We show comparison of the model with experimental magnetoresistance (MR) of MTJs and voltage degradation of MR with voltage. Proposed model enables MTJ circuit design that comprehends voltage dependent spin torque effects, switching error rates, spin degradation, and back hopping effects
Entanglement negativity in the critical Ising chain
International Nuclear Information System (INIS)
Calabrese, Pasquale; Tagliacozzo, Luca; Tonni, Erik
2013-01-01
We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix Tr(ρ A T 2 ) n and of the entanglement negativity for two spin blocks as a function of their length and separation in the critical Ising chain. For two adjacent blocks, we show that tensor network calculations agree with universal conformal field theory (CFT) predictions. In the case of two disjoint blocks the CFT predictions are recovered only after taking into account the finite size corrections induced by the finite length of the blocks. (paper)