Entanglement dynamics in critical random quantum Ising chain with perturbations
Huang, Yichen
2017-05-01
We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique.
Critical dynamics of cluster algorithms in the dilute Ising model
Hennecke, M.; Heyken, U.
1993-08-01
Autocorrelation times for thermodynamic quantities at T C are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation times decrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for which increasing autocorrelation times are expected.
Surface critical behavior of the smoothly inhomogeneous Ising model
Burkhardt, Theodore W.; Guim, Ihnsouk
1984-01-01
We consider a semi-infinite two-dimensional Ising model with nearest-neighbor coupling constants that deviate from the bulk coupling by Am-y for large m, m being the distance from the edge. The case ALeeuwen. We report exact results for the boundary magnetization and boundary pair-correlation function when A>0. At the bulk critical temperature there is a rich variety of critical behavior in the A -y plane with both paramagnetic and ferromagnetic surface phases. Some of our results can be derived and generalized with simple scaling arguments.
Static and dynamic critical behavior of thin magnetic Ising films
Sabogal-Suárez, D.; Alzate-Cardona, J. D.; Restrepo-Parra, E.
2015-09-01
This work presents a study of the effect of film thickness on the static and dynamic critical behavior of thin magnetic Ising films. Monte Carlo simulations using the Wolff algorithm were performed to determine the static and dynamic critical exponents of the films. A dimensionality crossover from 2D to 3D (due to the finiteness of the films) in the static and dynamic critical behavior was observed as the film thickness increases. In addition, a slight increase in the effective dimension deff and a considerable increase in the critical temperature Tc(∞) were found. Small values for the dynamic critical exponents were obtained, indicating that the Wolff algorithm is a very efficient method for these magnetic systems.
Critical Point of Ising Films with Different Growth Directions
Institute of Scientific and Technical Information of China (English)
WANG Huai-yu; ZHOU Yun-song; D.L.Lin
2000-01-01
The critical temperature Tc of a spin-l/2 Ising film of cubic structures is calculated by the variational cumulant expansion method for three directions of growth. The results from different growth directions are analysed and compared with each other. In the present model, the Tc values depend largely on the number of nearest neighbors in a monolayer for films with the same number of monolayers but grown in different directions. For sc, bcc and fcc structures, the highest Tc is found along the (100), (110), and (111) direction, respectively.
Entanglement dynamics in critical random quantum Ising chain with perturbations
Energy Technology Data Exchange (ETDEWEB)
Huang, Yichen, E-mail: ychuang@caltech.edu
2017-05-15
We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique. - Highlights: • We study the dynamical quantum phase transition between many-body localized phases. • We simulate the dynamics of a very long random spin chain with matrix product states. • We observe numerically super-logarithmic growth of entanglement entropy with time.
Critical Exponents of Ferromagnetic Ising Model on Fractal Lattices
Hsiao, Pai-Yi
2001-04-01
We review the value of the critical exponents ν-1, β/ν, and γ/ν of ferromagnetic Ising model on fractal lattices of Hausdorff dimension between one and three. They are obtained by Monte Carlo simulation with the help of Wolff algorithm. The results are accurate enough to show that the hyperscaling law df = 2β/ν + γ/ν is satisfied in non-integer dimension. Nevertheless, the discrepancy between the simulation results and the γ-expansion studies suggests that the strong universality should be adapted for the fractal lattices.
Roaming form factors for the tricritical to critical Ising flow
Horvath, D X; Takacs, G
2016-01-01
We study the massless flows described by the staircase model introduced by Al.B. Zamolodchikov through the analytic continuation of the sinh-Gordon S-matrix, focusing on the renormalisation group flow from the tricritical to the critical Ising model. We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow. As a by-product, we also construct form factors for a semi-local field in the sinh-Gordon model, which can be associated with the twist field in the ultraviolet limiting free massless bosonic theory.
Magnetic critical behavior of the Ising model on fractal structures
Monceau, Pascal; Perreau, Michel; Hébert, Frédéric
1998-09-01
The critical temperature and the set of critical exponents (β,γ,ν) of the Ising model on a fractal structure, namely the Sierpiński carpet, are calculated from a Monte Carlo simulation based on the Wolff algorithm together with the histogram method and finite-size scaling. Both cases of periodic boundary conditions and free edges are investigated. The calculations have been done up to the seventh iteration step of the fractal structure. The results show that, although the structure is not translationally invariant, the scaling behavior of thermodynamical quantities is conserved, which gives a meaning to the finite-size analysis. Although some discrepancies in the values of the critical exponents occur between periodic boundary conditions and free edges, the effective dimension obtained through the Rushbrooke and Josephson's scaling law have the same value in both cases. This value is slightly but significantly different from the fractal dimension.
Robust criticality of Ising model on rewired directed networks
Lipowski, Adam; Lipowska, Dorota
2015-01-01
We show that preferential rewiring, which is supposed to mimick the behaviour of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behaviour. For the non-rewired random graph version, due to a constant number of links out-going from each site, we write a simple mean-field-like equation describing the behaviour of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behaviour is traced back to the formation of a relatively small core of agents which influence the entire system.
Defects in the tri-critical Ising model
Makabe, Isao; Watts, Gérard M. T.
2017-09-01
We consider two different conformal field theories with central charge c = 7 /10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c = 7 /5, using the folding trick as first proposed by Gang and Yamaguchi [1]. We then act on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.
Conformal symmetry of the critical 3D Ising model inside a sphere
Cosme, Catarina; Penedones, Joao
2015-01-01
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.
Directory of Open Access Journals (Sweden)
Virve-Anneli Vihman
2010-01-01
Full Text Available Käesolevas artiklis vaadeldakse nimetavas käändes pronoomeni ise kasutamist internetifoorumites, kus on märkimisväärselt palju näiteid ise kasutustest ilma lähtevormita, s.t ilma nimi- või asesõnata, millele ise viitab. Artikli põhiküsimuseks on, kas ise-t kasutataksegi süstemaatiliselt isikulise pronoomeni asemel lause subjektina. Täpsemalt uurime, (a kas ise käitub subjekti kohatäitjana (paikneb subjekti positsioonis, kui lauses muud subjekti pole; (b kas ta käitub topikuna nagu tüüpiline isikuline asesõna lause algul, ning kas ta sealjuures kaotab ise-le omast rõhutavat, tähelepanu suunavat omadust ning (c kas ise-t kasutatakse eelkõige 1. isikule viitamisel. Korpusanalüüsist selgub, et ilma lähtevormita ise-t on kasutatud rohkem kui pooltes lausetes ning eriti sageli seoses 1. isiku väljendamisega. Samuti allub ise V2-reeglist tingitud inversioonile. Samas ei ole ka verbi ees kasutatud ise täielikult kaotanud rõhutavat funktsiooni. Ise kasutamine personaalse pronoomeni asemel subjekti positsioonis on ilmselt seotud negatiivsest (distantseerivast viisakusstrateegiast tingitud impersonaliseerimisega: vajadus rõhutavat, vastandavat 1. isiku pronoomenit vältida võib olla tinginud ise sagedase kasutamise subjekti positsioonis.
Nam, Keekwon; Kim, Bongsoo; Jong Lee, Sung
2014-08-01
We investigate the nonequilibrium relaxation dynamics of an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is known to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We performed a more detailed analysis of our extensive simulations on bigger lattice systems which reaffirms that the symmetry-breaking transition exhibits a non-Ising critical behavior with β ≃ 0.149(2) and η ≃ 0.30(1) that are distinct from those values of a pure two dimensional Ising model. Finite size scaling of dimer density near the symmetry breaking transition gives logarithmic scaling (α = 0.0) which is consistent with the hyperscaling relation but the corresponding exponent of νB ≃ 1.37(2) exhibits a conspicuous deviation from the pure Ising value of 1. The value of dynamic critical exponent z, however, is found to be close to that of the kinetic Ising model as 1/z ≃ 0.466(5) from the relaxation of staggered magnetization (and also similar but slightly smaller values from coarsening).
A Direct Calculation of Critical Exponents of Two-Dimensional Anisotropic Ising Model
Institute of Scientific and Technical Information of China (English)
XIONG Gang; WANG Xiang-Rong
2006-01-01
Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classicalIsing model (IM). We verify that the exponents are the same as those of isotropic classical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.
Fermionic coset realization of the critical Ising model
Cabra, D C; Rothe, K D
1995-01-01
We obtain an explicit realization of all the primary fields of the Ising model in terms of a conformal field theory of constrained fermions. The four-point correlators of the energy, order and disorder operators are explicitly calculated.
Polychromatic Arm Exponents for the Critical Planar FK-Ising model
Wu, Hao
2016-01-01
We derive the arm exponents of SLE$_{\\kappa}$ for $\\kappa\\in (4,8)$ and explain how to combine them with the convergence of the interface to obtain the arm exponents of critical FK-Ising model. We obtain six different patterns of boundary arm exponents and three different patterns of interior arm exponents of the critical planar FK-Ising model on the square lattice.
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
Binder, Kurt; Luijten, Erik
2001-04-01
A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one considers instead a long-range interaction described by a power-law decay, new classes of critical behavior depending on the exponent of this power law become accessible, and a stringent test of the ε-expansion becomes possible. As a final type of crossover from mean-field type behavior to two-dimensional Ising behavior, the interface localization-delocalization transition of Ising films confined between “competing” walls is considered. This problem is still hampered by questions regarding the appropriate coarse-grained model for the fluctuating interface near a wall, which is the starting point for both this problem and the theory of critical wetting.
Critical Dynamics Behavior of the Wolff Algorithm in the Site-Bond-Correlated Ising Model
Campos, P. R. A.; Onody, R. N.
Here we apply the Wolff single-cluster algorithm to the site-bond-correlated Ising model and study its critical dynamical behavior. We have verified that the autocorrelation time diminishes in the presence of dilution and correlation, showing that the Wolff algorithm performs even better in such situations. The critical dynamical exponents are also estimated.
Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
Coldea, R.; Tennant, D. A.; Wheeler, E M; Wawrzynska, E.; Prabhakaran, D.; Telling, M; Habicht, K.; Smeibidl, P; Kiefer, K.
2011-01-01
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb2O6 through its critical point using strong transv...
Critical behavior of a triangular lattice Ising AF/FM bilayer
Energy Technology Data Exchange (ETDEWEB)
Žukovič, M., E-mail: milan.zukovic@upjs.sk; Bobák, A.
2016-03-06
We study a bilayer Ising spin system consisting of antiferromagnetic (AF) and ferromagnetic (FM) triangular planes, coupled by ferromagnetic exchange interaction, by standard Monte Carlo and parallel tempering methods. The AF/FM bilayer is found to display the critical behavior completely different from both the single FM and AF constituents as well as the FM/FM and AF/AF bilayers. Namely, by finite-size scaling (FSS) analysis we identify at the same temperature a standard Ising transition from the paramagnetic to FM state in the FM plane that induces a ferrimagnetic state with a finite net magnetic moment in the AF plane. At lower temperatures there is another phase transition, that takes place only in the AF plane, to different ferrimagnetic state with spins on two sublattices pointing parallel and on one sublattice antiparallel to the spins on the FM plane. FSS indicates that the corresponding critical exponents are close to the two-dimensional three-state ferromagnetic Potts model values. - Highlights: • We study critical behavior of a triangular lattice Ising AF/FM bilayer. • Critical properties are studied by Monte Carlo and parallel tempering methods. • Critical exponents are determined from finite-size scaling analysis. • At higher temperature Ising phase transitions in both FM and AF layers are found. • At lower temperature a three-state Potts phase transition in AF layer is found.
Self-similar transformations of lattice-Ising models at critical temperatures
Feng, You-gang
2012-01-01
We classify geometric blocks that serve as spin carriers into simple blocks and compound blocks by their topologic connectivity, define their fractal dimensions and describe the relevant transformations. By the hierarchical property of transformations and a block-spin scaling law we obtain a relation between the block spin and its carrier's fractal dimension. By mapping we set up a block-spin Gaussian model and get a formula connecting the critical point and the minimal fractal dimension of the carrier, which guarantees the uniqueness of a fixed point corresponding to the critical point, changing the complicated calculation of critical point into the simple one of the minimal fractal dimension. The numerical results of critical points with high accuracy for five conventional lattice-Ising models prove our method very effective and may be suitable to all lattice-Ising models. The origin of fluctuations in structure at critical temperature is discussed. Our method not only explains the problems met in the renor...
Red-bond exponents of the critical and the tricritical Ising model in three dimensions
Deng, Youjin; Blöte, Henk W. J.
2004-11-01
Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p . These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc=1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr=0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr=1/2 for the latter model.
Critical Casimir forces between defects in the 2D Ising model
Nowakowski, P.; Maciołek, A.; Dietrich, S.
2016-12-01
An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.
Institute of Scientific and Technical Information of China (English)
Muktish Acharyya; Ajanta Bhowal Acharyya
2011-01-01
We solve the equilibrium meanfield equation of state of Ising ferromagnet (obtained from Bragg-Williams theory) by Newton-Raphson method.The number of iterations required to get a convergent solution (within a specified accuracy) of equilibrium magnetisation, at any particular temperature, is observed to diverge in a power law fashion as the temperature approaches the critical value.This is identified as the critical slowing down.The exponent is also estimated.This value of the exponent is compared with that obtained from analytic solution.Besides this, the numerical results are also compared with some experimental results exhibiting satisfactory degree of agreement.It is observed from this study that the information of the invariance of time scale at the critical point is present in the meanfield equilibrium equation of state of Ising ferromagnet.
Critical adsorption on defects in ising magnets and binary alloys
Hanke
2000-03-06
Long-range correlations in a magnet close to its critical point or in a binary alloy close to a continuous order-disorder transition can substantially enhance the effect of local perturbations. It is demonstrated using a position-space renormalization procedure that quasi-one-dimensional defects which break the symmetry of the order parameter have pronounced effects: They cause long-range critical adsorption profiles and give rise to new universal critical exponents, which are identified and calculated using field-theoretical methods.
Critical Adsorption on Defects in Ising Magnets and Binary Alloys
Hanke, Andreas
2000-03-01
Long-range correlations in a magnet close to its critical point or in a binary alloy close to a continuous order-disorder transition can substantially enhance the effect of local perturbations. It is demonstrated using a position-space renormalization procedure that quasi-one-dimensional defects which break the symmetry of the order parameter have pronounced effects: They cause long-range critical adsorption profiles and give rise to new universal critical exponents, which are identified and calculated using field-theoretical methods.
Locally converging algorithms for determining the critical temperature in Ising systems
Faraggi, Eshel; Robb, Daniel T.
2008-10-01
We introduce a class of algorithms that converge to criticality automatically, in a way similar to the invaded cluster algorithm. Unlike the invaded cluster algorithm which uses global percolation as a test for criticality, these local algorithms use an average over local observables, specifically the number of satisfied bonds, in a feedback loop which drives the system toward criticality. Two specific algorithms are introduced, the average algorithm and the locally converging Wolff algorithm. We apply these algorithms to study the Ising square lattice and the Ising Bethe lattice. We find reasonable convergence to the critical temperature for both systems under the locally converging Wolff algorithm. We also re-examine the phase diagram of the dilute two-dimensional (2D) Ising model and find results supporting our previously reported conclusions regarding the existence of a local regime of magnetization below the percolations threshold. In addition, the presented algorithms are computationally more efficient than the invaded cluster algorithm, requiring less CPU time and memory.
A Monte Carlo method for critical systems in infinite volume: the planar Ising model
Herdeiro, Victor
2016-01-01
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 functions 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.
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.
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-02-01
We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to 2-d Gravity
Bowick, M; Harris, G; Marinari, E
1994-01-01
We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
Universal free-energy distribution in the critical point of a random Ising ferromagnet.
Dotsenko, Victor; Holovatch, Yurij
2014-11-01
We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions Dcritical free-energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension D=3. It is demonstrated that this function is strongly asymmetric: its left tail is much slower than the right one.
Surface critical behavior of thin Ising films at the ‘special point’
Moussa, Najem; Bekhechi, Smaine
2003-03-01
The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.
Excited TBA equations II: massless flow from tricritical to critical Ising model
Energy Technology Data Exchange (ETDEWEB)
Pearce, Paul A. E-mail: p.pearce@ms.unimelb.edu.au; Chim, Leung E-mail: leung.chim@dsto.defence.gov.au; Ahn, Changrim E-mail: ahn@dante.ewha.ac.kr
2003-06-16
We consider the massless tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek{sub 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 massless 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{sub 4} lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.
Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice
Yamada, Hirofumi
2015-01-01
In Ising model on the simple cubic lattice, we describe the inverse temperature $\\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of those quantities are represented by the linear differential equations with constant coefficients which are related to critical exponents. We estimate the critical temperature and exponents via an expansion in the inverse powers of the mass under the use of $\\delta$-expansion. The critical inverse temperature $\\beta_{c}$ is estimated first in unbiased manner and then critical exponents are also estimated in biased and unbiased self-contained way including $\\omega$, the correction-to-scaling exponent, $\
Környei, László; Pleimling, Michel; Iglói, Ferenc
2008-01-01
The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.
Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions
Alves, G. A.; Vasconcelos, M. S.; Alves, T. F. A.
2016-04-01
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter qEA, the magnetic susceptibility χ , and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β ,γ , and ν . In the low-temperature limit we obtained a spin-glass phase with critical temperature around Tc≈2.274 , and the critical exponents β ,γ , and ν , indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.
Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures
Viteri, C. Ricardo; Tomita, Yu; Brown, Kenneth R.
2009-10-01
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.
Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures
Viteri, C Ricardo; 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.
Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model
Morales, Irving O.; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C.; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, Alejandro
2015-01-01
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point. PMID:26103513
Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model.
Directory of Open Access Journals (Sweden)
Irving O Morales
Full Text Available Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.
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Nascimento, Denise A. do, E-mail: denise.a.n@bol.com.br [Departamento de Fisica, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus-AM (Brazil); Departamento de Fisica, Universidade Federal de Roraima, BR 174, Km 12. Bairro Monte Cristo, CEP: 69300-000 Boa Vista/RR (Brazil); Neto, Minos A., E-mail: minosneto@hotmail.com [Departamento de Fisica, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus-AM (Brazil); Ricardo de Sousa, J., E-mail: jsousa@edu.ufam.br [Departamento de Fisica, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus-AM (Brazil); National Institute of Science and Technology for Complex Systems, 3000, Japiim, 69077-000 Manaus-AM (Brazil); Pacobahyba, Josefa T., E-mail: jtmpacobahyba@dfis.ufrr.br [Departamento de Fisica, Universidade Federal de Roraima, BR 174, Km 12. Bairro Monte Cristo, CEP: 69300-000 Boa Vista/RR (Brazil)
2012-08-15
In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H) and transverse ({Omega}) fields by using the effective-field theory. The model consists of ferromagnetic interaction J{sub x} in the x direction and antiferromagnetic interaction J{sub y} in the y direction in the presence of the H and {Omega} fields. We obtain the phase diagrams in the H-T and {Omega}-T planes changing values of the {Omega} and H parameters, respectively for fixed value at {lambda}=J{sub x}/J{sub y}=1. At null temperature, the ground state phase diagram in the {Omega}-H plane for several values of {lambda} parameter is analyzed. In the particular case of {lambda}=1 we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field H{sub c}/J{sub y}=2.0 for {Omega}=0 by using EFT. - Highlights: Black-Right-Pointing-Pointer In the last decade there has been a great interest in physics of the quantum phase transition in system at low dimensional. Black-Right-Pointing-Pointer In particular, the transverse Ising model has been studied by a variety of approximate methods. Black-Right-Pointing-Pointer In the context of quantum phase transition and critical phenomena. Black-Right-Pointing-Pointer First time, is presented a study of the superantiferromagnetic transverse Ising model on an anisotropic square lattice. Black-Right-Pointing-Pointer We have obtained finite temperature and ground state phase diagrams.
Universal critical behavior of the two-dimensional Ising spin glass
Fernandez, L. A.; Marinari, E.; Martin-Mayor, V.; Parisi, G.; Ruiz-Lorenzo, J. J.
2016-07-01
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
Pinho, S. T. R.; Haddad, T. A. S.; Salinas, S. R.
We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuations.
Dolfi, M; Hehn, A; Imriška, J; Pakrouski, K; Rønnow, T F; Troyer, M; Zintchenko, I; Chirigati, F; Freire, J; Shasha, D
2014-01-01
In this paper we present a simple, yet typical simulation in statistical physics, consisting of large scale Monte Carlo simulations followed by an involved statistical analysis of the results. The purpose is to provide an example publication to explore tools for writing reproducible papers. The simulation estimates the critical temperature where the Ising model on the square lattice becomes magnetic to be Tc /J = 2.26934(6) using a finite size scaling analysis of the crossing points of Binder cumulants. We provide a virtual machine which can be used to reproduce all figures and results.
Criticality in Alternating Layered Ising Models : I. Effects of connectivity and proximity
Au-Yang, Helen; Fisher, Michael E.
2013-01-01
The specific heats of exactly solvable alternating layered planar Ising models with strips of width $m_1$ lattice spacings and ``strong'' couplings $J_1$ sandwiched between strips of width $m_2$ and ``weak'' coupling $J_2$, have been studied numerically to investigate the effects of connectivity and proximity. We find that the enhancements of the specific heats of the strong layers and of the overall or `bulk' critical temperature, $T_c(J_1,J_2;m_1,m_2)$, arising from the collective effects r...
Unusual finite size effects on critical temperature in fcc Ising antiferromagnets
Pommier, J.; Diep, H. T.; Ghazali, A.; Lallemand, P.
1988-04-01
A new multispin coding technique is presented for Monte Carlo simulation of antiferromagnetic Ising spin systems on an fcc lattice. The nearest- and next-nearest-neighbor interactions J1 and J2 are included. This technique allows a considerable gain in CPU time and computer memory. As a first application, we have studied samples of 4L3 spins with L up to 48. An unusual behavior of the critical temperature with increasing L is found in the case of nearest-neighbor interaction in zero field. Finite size effects on the locations of tricrical points in the (T,J2/J1) plane are discussed.
Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient
Muglia, J.; Albano, E. V.
2012-08-01
In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures T 1 T c ) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization m ≡ 0 corresponding to T = ∞, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization m = m 0, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T = 0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ( t → ∞) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.
Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry.
Coldea, R; Tennant, D A; Wheeler, E M; Wawrzynska, E; Prabhakaran, D; Telling, M; Habicht, K; Smeibidl, P; Kiefer, K
2010-01-08
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.
DEFF Research Database (Denmark)
Schwahn, D.; Mortensen, K.; Frielinghaus, H.;
2000-01-01
Thermal composition fluctuations and the associated crossover from the 3D-Ising to the isotropic Lifshitz universality class have been studied in a three-component mixture made of a critical polymer blend and the corresponding diblock copolymer. The rather complex phase diagram and the critical...
Murase, Yohsuke; Ito, Nobuyasu
2008-01-01
Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λm (=β/zν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.
Conformal perturbation of off-critical correlators in the 3D Ising universality class
Caselle, Michele; Magnoli, Nicodemo
2016-01-01
Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the $$, $$ and $$ two point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the $s = t r^{\\Delta_{t}}$ expansion, where $t$ is the reduced temperature. Our results for $$ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.
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Takamoto, Masahiro [Department of Applied Quantum Physics, Kyushu University, Fukuoka 812-8581 (Japan)]. E-mail: masahtap@mbox.nc.kyushu-u.ac.jp; Muraoka, Yoshinori [Department of General Education, Ariake National College of Technology, Omuta, Fukuoka 836-8585 (Japan); Idogaki, Toshihiro [Department of Applied Quantum Physics, Kyushu University, Fukuoka 812-8581 (Japan)
2007-03-15
Using Monte Carlo simulation with the Wolff algorithm and single histogram method, the critical behavior of the ferromagnetic Ising thin films with thickness ranging from n=3 to 15 layers, has been studied. With varying the ratio of surface interaction to bulk one, {kappa}=J{sub s}/J{sub B}, we found a special point {kappa}{sub sp} at which all the film have a unique critical temperature independent of film thickness n. In the region that {kappa} is less than {kappa}{sub sp}, the shift exponent {lambda} is independent of {kappa} in the limit n->{approx}, but the strength of surface coupling strongly affects the gradient of asymptotic curve {lambda} vs 1/n. When {kappa} is larger than {kappa}{sub sp}, however, the clear power law behavior is not found.
Takamoto, Masahiro; Muraoka, Yoshinori; Idogaki, Toshihiro
2007-03-01
Using Monte Carlo simulation with the Wolff algorithm and single histogram method, the critical behavior of the ferromagnetic Ising thin films with thickness ranging from n=3 to 15 layers, has been studied. With varying the ratio of surface interaction to bulk one, κ=Js/JB, we found a special point κsp at which all the film have a unique critical temperature independent of film thickness n. In the region that κ is less than κsp, the shift exponent λ is independent of κ in the limit n→∞, but the strength of surface coupling strongly affects the gradient of asymptotic curve λ vs 1/n. When κ is larger than κsp, however, the clear power law behavior is not found.
Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
Patel, Aavishkar A; Sachdev, Subir
2016-01-01
In a strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\\hbar)\\, \\eta/s$, where $\\eta$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $\\eta$ scales in the same manner as a chiral conductivity, and the ratio $\\eta/s$ diverges as $T^{-2/z}$, where $z$ is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.
Hobrecht, Hendrik
2016-01-01
We present a systematic method to calculate the scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function $Z$ on an $L\\times M$ square lattice, wrapped around a torus with aspect ratio $\\rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2\\times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $\\rho\\to 0$. Additionally, for the cylinder at criticality our result confirms the predictions...
Critical properties of short-range Ising spin glasses on a Wheatstone-bridge hierarchical lattice.
Almeida, Sebastião T O; Nobre, Fernando D
2015-08-01
An Ising spin-glass model with nearest-neighbor interactions, following a symmetric probability distribution, is investigated on a hierarchical lattice of the Wheatstone-bridge family characterized by a fractal dimension D≈3.58. The interaction distribution considered is a stretched exponential, which has been shown recently to be very close to the fixed-point coupling distribution, and such a model has been considered lately as a good approach for Ising spin glasses on a cubic lattice. An exact recursion procedure is implemented for calculating site magnetizations, mi=〈Si〉T, as well as correlations between pairs of nearest-neighbor spins, 〈SiSj〉T (〈〉T denote thermal averages), for a given set of interaction couplings on this lattice. From these local magnetizations and correlations, one can compute important physical quantities, such as the Edwards-Anderson order parameter, the internal energy, and the specific heat. Considering extrapolations to the thermodynamic limit for the order parameter, such as a finite-size scaling approach, it is possible to obtain directly the critical temperature and critical exponents. The transition between the spin-glass and paramagnetic phases is analyzed, and the associated critical exponents β and ν are estimated as β=0.82(5) and ν=2.50(4), which are in good agreement with the most recent results from extensive numerical simulations on a cubic lattice. Since these critical exponents were obtained from a fixed-point distribution, they are universal, i.e., valid for any coupling distribution considered.
Şarlı, Numan
2015-01-01
The effects of the magnetic atom number in the unit volume on the magnetic properties are investigated by using sc (n=8), bcc (n=9) and fcc (n=14) Ising NLs within the effective field theory with correlations. We find that the magnetic properties expand as the magnetic atom number increases in the unit volume and this expanding constitutes an elliptical path at TC. The effect of the magnetic atom number (n) in the unit volume on the magnetic properties (mp) appear as nscconstant is directly proportional with the atom number in the unit volume (C α n). Hence, by using the slopes of the paramagnetic hysteresis curves of any nanosystem, it can be predicted that the number of particles in its unit volume. Moreover, the magnetic atoms in the paramagnetic region can be considered as particles in the gas. Because of the absence of an external magnetic field, the spin orientations of these atoms are random and free to rotate. Hence, they act on individually with no mutual interaction between two nearest-neighbor magnetic atoms. Therefore, we use the statistical mechanics form of the ideal gas law in the paramagnetic region and we obtain the critical paramagnetic pressure (PC=npkBTC) of the Ising NLs at TC. We define the paramagnetic magnetic atom number in the unit volume as np=n(1-M(T)).
Thermal properties and Ising critical behavior in EuFe{sub 2}As{sub 2}
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Oleaga, A., E-mail: alberto.oleaga@ehu.es [Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alameda Urquijo s/n, 48013 Bilbao (Spain); Salazar, A. [Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alameda Urquijo s/n, 48013 Bilbao (Spain); Thamizhavel, A.; Dhar, S.K. [Department of Condensed Matter Physics and Material Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005 (India)
2014-12-25
Highlights: • A high resolution ac photopyroelectric calorimeter is used. • Thermal diffusivity and specific heat are measured at the phase transitions. • Latent heat is exchanged at the Fe{sup 2+} spin-ordering transition. • Eu{sup 2+} spin-ordering transition belongs to the 3D-Ising universality class. - Abstract: Specific heat and thermal diffusivity have been studied by means of a high resolution ac photopyroelectric calorimeter in the vicinity of phase transitions in EuFe{sub 2}As{sub 2}: the first one corresponding to the ordering of the Fe{sup 2+} spins concomitant to a structural transition at 188.1 K and the second one to the antiferromagnetic ordering of the Eu{sup 2+} spins at 18.4 K. The weak first order character of the first transition has been confirmed while the critical behavior of the second transition at lower temperature has been established to correspond to the 3D-Ising universality class (α{sub exp} = 0.11 ± 0.03). This is in agreement with the proposed uniaxial arrangement of the Eu{sup 2+} spins lying along the long orthorhombic axis a as reported in literature.
Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs
Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
2016-11-01
We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.
Local and cluster critical dynamics of the 3d random-site Ising model
Ivaneyko, D.; Ilnytskyi, J.; Berche, B.; Holovatch, Yu.
2006-10-01
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.
Motif based hierarchical random graphs: structural properties and critical points of an Ising model
Kotorowicz, M; 10.5488/CMP.14.13801
2011-01-01
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824-827]. The construction scheme resembles that used in [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, 73, 066126], according to which the short-range bonds are non-random, whereas the long-range bonds appear independently with the same probability. A number of structural properties of the graphs have been described, among which there are degree distributions, clustering, amenability, small-world property. For one of the motifs, the critical point of the Ising model defined on the corresponding graph has been studied.
Orlandi, A.; Parola, A.; Reatto, L.
2004-11-01
We study how the formalism of the hierarchical reference theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid-state theory which implements the basic ideas of the Wilson momentum-shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and nonclassical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the nonuniversal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.
Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction
Horita, Toshiki; Suwa, Hidemaro; Todo, Synge
2017-01-01
We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, Ji j=|r⃗i-r⃗j| -(d +σ ) , where d (=2) is the dimension of the system and σ is the decay exponent, by means of the order-N cluster-algorithm Monte Carlo method. In particular, we focus on the upper and lower critical decay exponents, the boundaries between the mean-field-universality, intermediate, and short-range-universality regimes. At the critical decay exponents, it is found that the standard Binder ratio of magnetization at the critical temperature exhibits extremely slow convergence as a function of the system size. We propose more effective physical quantities, namely the combined Binder ratio and the self-combined Binder ratio, both of which cancel the leading finite-size corrections of the conventional Binder ratio. Utilizing these techniques, we clearly demonstrate that in two dimensions, the lower and upper critical decay exponents are σ =1 and 7/4, respectively, contrary to the recent Monte Carlo and renormalization-group studies [M. Picco, arXiv:1207.1018; T. Blanchard et al., Europhys. Lett. 101, 56003 (2013) 10.1209/0295-5075/101/56003].
Short-time critical dynamics of damage spreading in the two-dimensional Ising model
Rubio Puzzo, M. Leticia; Albano, Ezequiel V.
2010-05-01
The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at T=∞ and magnetization M=0 , an initial damage is created by flipping a small amount of spins in one of the two replicas studied. In this way, the initial damage is proportional to the initial magnetization M0 in one of the configurations upon quenching the system at TC , the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent θD=1.915(3) , which is much larger than the exponent θ=0.197 characteristic of the initial increase of the magnetization M(t) . Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic (⟨R2(t)⟩) grows with an exponent z∗≈η≈1.9 , which is the same, within error bars, as the exponent θD . However, the survival probability of the epidemics reaches a plateau so that δ=0 . On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at TD≃0.51TC , where all the measured observables exhibit power laws with exponents θD=1.026(3) , δ=0.133(1) , and z∗=1.74(3) .
Critical behaviour of the Ising ferromagnet confined in quasi-cylindrical pores: A Monte Carlo study
Guisandez, Leandro E.; Zarragoicoechea, Guillermo J.; Albano, Ezequiel V.
2013-10-01
The critical behaviour of the Ising ferromagnet confined in pores of radius R and length L is studied by means of Monte Carlo computer simulations. Quasi-cylindrical pores are obtained by replicating n-times a triangular lattice disc of radius R, where L = na and a is the spacing between consecutive replications. So, spins placed at the surface of the pores have less nearest-neighbours (NN) as compared to 8 NN for spins in the bulk. These "missing neighbour" effects undergone by surface spins cause a strong suppression of surface ordering, leading to an ordinary surface transition. Also, the effect propagates into the bulk for small tubes (R ⩽ 12) and the effective critical temperature of the pores is shifted towards lower values than in the bulk case. By applying the standard finite-size scaling theory, subsequently supported by numerical data, we concluded that data collapse of relevant observables, e.g., magnetization (m), susceptibility, specific heat, etc., can only be observed by comparing simulation results obtained by keeping the aspect ratio C ≡ R/L constant. Also, by extrapolating "effective" R-dependent critical temperatures to the thermodynamic limit (R → ∞, C fixed), we obtained TC(∞) = 6.208(4). As suggested by finite-size scaling arguments, the magnetization is measured at the critical point scales according to _{T_c}R^{β /ν }∝ [R/L]^ {1/2}, where β and ν are the standard exponents for the order parameter and the correlation length, respectively. Furthermore, it is shown that close to criticality the axial correlation length decreases exponentially with the distance. That result is the signature of the formation of (randomly distributed) alternating domains of different magnetization, which can be directly observed by means of snapshot configurations, whose typical length (ξ) is given by the characteristic length of the exponential decay of correlations. Moreover, we show that at criticality ξ = 0.43(2)R.
Critical wetting in the two-dimensional Ising ferromagnet confined between inhomogeneous walls
Trobo, Marta L.; Albano, Ezequiel V.
2014-12-01
We present a numerical study of the critical wetting behavior of an Ising magnet confined between two walls, separated by a distance L, where short-range inhomogeneous surface magnetic fields act. So, samples are assumed to have a size L × M, L being the width and M the length, respectively. By considering surface fields varying spatially with a given wavelength or period (λ), H1(x,λ) with 1 ≤ x ≤ M, we found that the wetting temperature is given by the exact result of Abraham [D.B. Abraham, Phys. Rev. Lett. 44, 1165 (1980)] provided that an effective field given by the spacial average[-3.4mm] value (Heff ≡ 1/λ ƒ0 λH1(x,λ)dx > 0) is considered. The above results hold in the low wavelength regime, while for λ → ∞ and a bivaluated surface field (i.e., Hmax for x ≤ M/ 2, and δHmax for x>M/ 2, with 0 <δ< 1), one observes two almost independent wetting transitions, both being compatible with Abraham's exact results corresponding to Hmax and δHmax, respectively. On the other hand, for H1(x,λ) ≠ 0 but Heff = 0 bulk standard critical behavior results is observed.
Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
Hobrecht, Hendrik; Hucht, Alfred
2017-02-01
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
2012-09-14
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
Institute of Scientific and Technical Information of China (English)
B. Kutlu; M. Civi
2006-01-01
@@ We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice under periodic boundary conditions.
Roters, L; Lübeck, S; Usadel, K D
2002-12-01
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality, the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.
Tsai, Shan-Ho; Wang, Fugao; Landau, D P
2007-06-01
Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.
2007-06-01
Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
The crossover from mean-field to 3D-Ising critical behaviour in a 3-component microemulsion
DEFF Research Database (Denmark)
Seto, H.; Schwahn, D.; Yokoi, E.
1995-01-01
Density fluctuations and associated critical phenomena of water droplets in a water-in-oil microemulsion system have been studied, We have recently found a mean-field behavior in the ''near-critical region'', and this evidence suggested that a crossover from mean-field to non-mean-field behavior...... should be observed. Therefore, a measurement of small-angle neutron scattering was carried out at JAERI with more precise temperature steps. Indeed, the crossover from mean-held to 3D-Ising behavior was observed, and the result could be interpreted by the asymptotic crossover theory proposed by Belyakov...
CRITICAL BEHAVIOR OF S-3／2 ISING MODEL IN RANDOM LONGITUDINAL AND TRANSVERSE FIELDS
Institute of Scientific and Technical Information of China (English)
宋为基
1995-01-01
The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).
Institute of Scientific and Technical Information of China (English)
WANG Xian-Zhi
2001-01-01
Using the numerical results and some results from the renormalization group theory, we extend our previous approach of determining the Yang-Lee edge singularities of Ising ferromagnets on square, triangular and honeycomb lattices (Phys. Rev. Lett. 78 (1997) 413; Phys. Rev. E56 (1998) 2793; E57 (1998) 5013) and obtain accurate closed-form approximations of the critical lines of anisotropic Ising ferromagnets on these lattices.
Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji
2012-09-01
We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.
Lopes Cardozo, David; Holdsworth, Peter C. W.
2016-04-01
The magnetization probability density in d = 2 and 3 dimensional Ising models in slab geometry of volume L\\paralleld-1× {{L}\\bot} is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio ρ =\\frac{{{L}\\bot}}{{{L}\\parallel}} and boundary conditions are discussed. In the limiting case ρ \\to 0 of a macroscopically large slab ({{L}\\parallel}\\gg {{L}\\bot} ) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.
Hartford, Edward John
This position-space renormalization-group study focuses on two systems with quenched disorder: the Ising spin glass and the asymmetric random-field Ising model. We have employed the Migdal-Kadanoff approach to determine local recursion relations and have retained the full correlated probability distribution of interactions and fields at each iteration in a series of histograms. We find an equilibrium spin-glass phase in three dimensions, but not in two. The spin glass is characterized by a distribution of effective interactions that broadens under iteration, signaling both the long-range order of the phase and the importance of competing interactions on all length scales. We have introduced a method to calculate the distribution of local properties by differentiating the free energy with respect to a particular magnetic field or interaction. Within the spin-glass phase, the nearest neighbor correlation ranges from negative one to one, showing the strong correlations and the local variation within the phase. The spin-glass-to-paramagnet phase transition is second order, with a smooth specific heat indicated by a negative critical exponent alpha. The multicritical point separating the spin-glass, paramagnetic, and ferromagnetic phases lies along the Nishimori line and also has a nondivergent specific heat. When the system undergoes quenched dilution, the resulting critical and multicritical behaviors are identical to those of the undiluted system. Even the addition of an infinitesimal magnetic field destroys the long-range spin-glass order; however, the characteristic broadening of the distribution continues for several iterations for small fields and low temperatures, suggesting the persistence of sizable spin-glass domains. Our study of the asymmetric random-field Ising model is motivated by recent experiments on phase transitions in porous media and mean-field treatments, which suggest that new critical behavior could occur when the distribution of fields is
Monte Carlos studies of critical and dynamic phenomena in mixed bond Ising model
Santos-Filho, J. B.; Moreno, N. O.; de Albuquerque, Douglas F.
2010-11-01
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; YAN Shi-Lei
2006-01-01
Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-ion anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T-Ω1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T-Ω1 space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T-D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.
Finite-temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
Punk, Matthias
2016-11-01
We study finite-temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent z =2 , in contrast to z =3 found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to Ω /γ (T ) at small momenta, where γ (T ) is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte Carlo simulations at finite temperature, where results consistent with z =2 were found.
Rodriguez, D. E.; Bab, M. A.; Albano, E. V.
2011-09-01
Extensive Monte Carlo simulations are employed in order to study the dynamic critical behaviour of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form 1/rd + σ, with σ = 0.75. The critical temperature, as well as the critical exponents, are evaluated from the power-law behaviour of suitable physical observables when the system is quenched from uncorrelated states, corresponding to infinite temperature, to the critical point. These results are compared with those obtained from the dynamic evolution of the system when it is annealed at the critical point from the ordered state. Also, the critical temperature in the infinite interaction limit is obtained by means of a finite-range scaling analysis of data measured with different truncated interaction ranges. All the estimated static critical exponents (γ/ν, β/ν, and 1/ν) are in good agreement with renormalization group (RG) results and previously reported numerical data obtained under equilibrium conditions. On the other hand, the dynamic exponent of the initial increase of the magnetization (θ) was close to RG predictions. However, the dynamic exponent z of the time correlation length is slightly different to the RG results probably due to the fact that it may depend on the specific dynamics used or because the two-loop expansion used in the RG analysis may be insufficient.
Nam, Keekwon; Park, Sangwoong; Kim, Bongsoo; Jong Lee, Sung
2011-06-01
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 Z2 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.
Critical behavior of the mixed-spin Ising model with two competing dynamics.
Godoy, Mauricio; Figueiredo, Wagner
2002-02-01
In this work we investigate the stationary states of a nonequilibrium mixed-spin Ising model on a square lattice. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T and subject to an external flux of energy. The contact with the heat bath is simulated by single spin flips according to the Metropolis rule, while the input of energy is mimicked by the simultaneous flipping of pairs of neighboring spins. We performed Monte Carlo simulations on this model in order to find its phase diagram in the plane of temperature T versus the competition parameter between one- and two-spin flips, p. The phase diagram of the model exhibits two ordered phases with sublattice magnetizations m(1), m(2)>0 and m(1)>0, m(2)model belongs to the universality class of the two-dimensional equilibrium Ising model.
Liu, R. M.; Zhuo, W. Z.; Chen, J.; Qin, M. H.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.
2017-07-01
We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Butera, P
2002-01-01
We have extended through beta^{23} the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover the expansions for the nearest-neighbor correlation function, the susceptibility and the second correlation moment have been extended up to beta^{25}. Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyper-universal combinations of critical amplitudes such as the renormalized four-point coupling g_r or the quantity usually denoted by R^{+}_{xi}. We have used a variety of series extrapolation procedures and, in some of the analyses, we have assumed that the leading correction-to-scaling exponent theta is universal and roughly known. We have also verified, to high precision, the validity of the hyperscaling relation and of the universality property both with regard to the lattice structure and to ...
Institute of Scientific and Technical Information of China (English)
YAN ShiLei; DENG LingLing; YANG ChuanZhang
2001-01-01
The critical properties of the bond-diluted mixed spin-1/2 and spin-1 transverse Ising system with singleion anisotropy are investigated by means of the effective field theory with correlations. Particular emphasis is given to the square lattice for which phase diagrams are obtained. If transverse field varies in the certain ranges we find that the tricritical point is obtained for the value of the bond concentration in a restricted region. We also observe that the reentrant phase transition may occur in the present system if single-ion anisotropy parameter is not large and if transverse field is small. On the other hand, for certain values of the system parameters, new induced magnetic ordering can be obtained. We find a number of interesting phenomena that are not predicted by previous literatures. The influence of the transverse field on the behaviours of the reentrant phase transition and induced magnetic ordering is discussed. A detailed description of the phase transition is presented.``
Butera, P
2003-01-01
For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have computed for the first time various critical parameters and improved the estimates of others. Moreover the properties of hyperscaling and of universality (spin S independence) of exponents and of various dimensionless amplitude combinations have been verified accurately. Assuming the validity of the lattice-lattice scaling, from our estimates of critical amplitudes for the square lattice we have also obtained estimates of the corresponding amplitudes for the spin S Ising model on the triangular, honeycomb, and kagome` lattices.
Critical point scaling of Ising spin glasses in a magnetic field
Yeo, Joonhyun; Moore, M. A.
2015-03-01
Critical point scaling in a field H applies for the limits t →0 (where t =T /Tc-1 ) and H →0 but with the ratio R =t /H2 /Δ finite. Δ is a critical exponent of the zero-field transition. We study the replicon correlation length ξ and from it the crossover scaling function f (R ) defined via 1 /(ξ H4 /(d +2 -η )) ˜f (R ) . We have calculated analytically f (R ) for the mean-field limit of the Sherrington-Kirkpatrick model. In dimension d =3 , we have determined the exponents and the critical scaling function f (R ) within two versions of the Migdal-Kadanoff (MK) renormalization group procedure. One of the MK versions gives results for f (R ) in d =3 in reasonable agreement with those of the Monte Carlo simulations at the values of R for which they can be compared. If there were a de Almeida-Thouless (AT) line for d ≤6 , it would appear as a zero of the function f (R ) at some negative value of R , but there is no evidence for such behavior. This is consistent with the arguments that there should be no AT line for d ≤6 , which we review.
Institute of Scientific and Technical Information of China (English)
LIU Meitang; MU Bozhong
2005-01-01
The critical adsorbing properties in slits and three-dimension (3D) phase transitions can be predicted by either Freed theory or Flory-Huggins theory. The mean field approximation in Flory-Huggins theory may cause apparent system errors, from which one can observe two-dimension (2D) phase transitions although it is not true. Monte Carlo simulation has demonstrated that Freed theory is more suitable for predicting adsorbing properties of fluids in slits than Flory-Huggins theory. It was found that from Freed theory prediction multilevel adsorption occurs in slits and the spreading pressure curves exhibit binodal points.
Gallo, Paola; Sciortino, Francesco
2012-10-26
We present a finite-size scaling study of the liquid-liquid critical point in the Jagla model, a prototype model for liquids that present the same thermodynamic anomalies which characterize liquid water. Performing successive umbrella sampling grand canonical Monte Carlo simulations, we evaluate an accurate density of states for different system sizes and determine the size-dependent critical parameters. Extrapolation to infinite size provides estimates of the bulk critical values for this model. The finite-size study allows us to establish that critical fluctuations are consistent with the Ising universality class and to provide definitive evidence for the existence of a liquid-liquid critical point in the Jagla potential. This finding supports the possibility of the existence of a genuine liquid-liquid critical point in anomalous one-component liquids like water.
Hoede, C.; Zandvliet, H.J.W.
2008-01-01
In a recent paper Hoede and Zandvliet introduced the concept of gauging on an equation. This enables the simulation of more complex Ising models by the simple quadratic model. The possibility of simulating the simple cubic model was defended by calculating a sequence of approximations to the transit
Quantum criticality and Lifshitz transition in the Ising system CeRu2Si2: Comparison with YbRh2Si2
Pourret, A.; Aoki, D.; Boukahil, M.; Brison, J. -P.; Knafo, W.; Knebel, G.; Raymond, S.; Taupin, M.; Onuki, Y.; Flouquet, J.
2013-01-01
New thermoelectric power (TEP) measurements on prototype heavy-fermion compounds close to magnetic quantum criticality are presented. The highly sensitive technique of TEP is an unique tool to reveal Fermi surface instabilities, referred here as Lifshitz transitions. The first focus is on the Ising CeRu2Si2 series. Doping CeRu2Si2 with Rh produces a decoupling between the first order metamagnetic transition and the pseudo-metamagnetism observed in the pure compound. Comparison is made with th...
SL(2,Z)-invariance and D-instanton contributions to the D^6R^4 interaction
Green, M B; Vanhove, P
2014-01-01
The modular invariant coefficient of the $D^6R^4$ interaction in the low energy expansion of type IIB string theory has been conjectured to be a solution of an inhomogeneous Laplace eigenvalue equation, obtained by considering the toroidal compactification of two-loop Feynman diagrams of eleven-dimensional supergravity. In this paper we determine its exact $SL(2,\\mathbb Z)$-invariant solution $f(\\Omega)$ as a function of the complex modulus, $\\Omega=x+iy$, satisfying an appropriate moderate growth condition as $y\\to \\infty$ (the weak coupling limit). The solution is presented as a Fourier series with modes $\\widehat{f}_n(y) e^{2\\pi i n x}$, where the mode coefficients, $\\widehat{f}_n(y)$ are bilinear in $K$-Bessel functions. Invariance under $SL(2,\\mathbb Z)$ requires these modes to satisfy the nontrivial boundary condition $ \\widehat{f}_n(y) =O(y^{-2})$ for small $y$, which uniquely determines the solution. The large-$y$ expansion of $f(\\Omega)$ contains the known perturbative (power-behaved) terms, together...
Quantum Criticality and Lifshitz Transition in the Ising System CeRu2Si2: Comparison with YbRh2Si2
Pourret, Alexandre; Aoki, Dai; Boukahil, Mounir; Brison, Jean-Pascal; Knafo, William; Knebel, Georg; Raymond, Stephane; Taupin, Mathieu; Ōnuki, Yoshichika; Flouquet, Jacques
2014-06-01
New thermoelectric power (TEP) measurements on prototype heavy-fermion compounds close to magnetic quantum criticality are presented. The highly sensitive technique of TEP is an unique tool to reveal Fermi surface instabilities, referred here as Lifshitz transitions. The first focus is on the Ising CeRu2Si2 series. Doping CeRu2Si2 with Rh produces a decoupling between the first order metamagnetic transition and the pseudo-metamagnetism observed in the pure compound. Comparison is made with the case of YbRh2Si2 which is often considered as the archetype of local quantum criticality by contrast to CeRu2Si2, taken as an example of spin-density wave criticality. Up to now for ferromagnetic materials showing ferromagnetic wings, no simple case appears where the Fermi surface is preserved between the ferromagnetic and paramagnetic phases. An open issue is the consequence of Lifshitz transitions on superconductivity in these multiband systems.
A Solvable Decorated Ising Lattice Model
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A decoratedlattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found atK1 = 0.5769, K2 = -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.
Yin, Junqi; Landau, David
2010-03-01
Using the parallel tempering algorithm and GPU accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising (lattice gas) model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Possibility of the XY-like transition is examined and both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase turn out to be continuous. From our data analysis, reentrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the non-universal critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.
Kastening, Boris
2012-10-01
Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With ξ(>) the largest and ξ(temperature near criticality, we find that the dependence of these functions on the ratio ξ() and on the angle parametrizing the orientation of the correlation volume is of geometric nature. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film (i.e., in an L×∞(d-1) geometry) with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for weakly anisotropic systems.
Alzate-Cardona, Juan David; Barrero-Moreno, María Camila; Restrepo-Parra, Elisabeth
2017-09-04
In this work, Monte Carlo simulations based on Metropolis algorithm were performed to study the critical and compensation temperatures of a core-shell nanowire with spins S=±5/2,±3/2,±1/2 and σ=±3/2,±1/2, respectively, considering an Ising antiferromagnetic system. The influence of nearest neighbors exchange interactions and crystal field anisotropy on the critical and compensation behaviors of the system has been analyzed. The effects of the nanowire height in the critical and compensation temperatures were evaluated. The results show that, for a system with given values of exchange interaction constants and crystal field anisotropy, a compensation point only appears if two requirements are satisfied. First, the weight of the core magnetization in the total magnetization must be greater than the weight of the shell magnetization at zero temperature. And second, the exchange constant of shell ions must be greater than a certain value. This value is, at the same time, greater than the exchange constant of core ions. The critical and compensation temperatures are very sensitive to variations in the exchange constant of the shell ions and core ions, respectively, while the crystal field anisotropy affects both temperatures. © 2017 IOP Publishing Ltd.
Murtazaev, A. K.; Ramazanov, M. K.; Kurbanova, D. R.; Badiev, M. K.; Abuev, Ya. K.
2017-06-01
The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J 2/ J 1 in the range of k ∈ [0.0, 1.0] with the step Δ k = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].
Baillie, C F; Kownacki, J P
1994-01-01
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For antiferromagnetic couplings the replica trick gives some evidence for a spin glass phase. In this paper we investigate both the ferromagnetic and antiferromagnetic models with the aid of simulations. We confirm the Bethe lattice values of the critical points for the ferromagnetic model on \\phi^3 and \\phi^4 graphs and examine the putative spin glass phase in the antiferromagnetic model by looking at the overlap between replicas in a quenched ensemble of graphs. We also compare the Ising results with those for higher state Potts models and Ising models on ``fat'' graphs, such as those used in 2D gravity simulations.
DEFF Research Database (Denmark)
Seto, H.; Schwahn, D.; Nagao, M.
1996-01-01
Critical density fluctuations of water droplets in an oil-rich three-component microemulsion system have been studied by small-angle neutron scattering as a function of temperature near and far from the boundary of phase decomposition. The observed data in the one-phase region are well described...
Ising Transition in Dimerized XY Quantum Spin Chain
Institute of Scientific and Technical Information of China (English)
YE Fei; DING Guo-Hui; XU Bo-Wei
2002-01-01
We proposed a simple spin-1/2 model which provides an exactly solvable example to study the Ising criticality with central charge c = 1/2.By mapping it onto the real Majorana fermions,the Ising critical behavior is explored explicitly,although its bosonized form is not the double frequency sine-Gordon model.
Topological transitions in Ising models
Jalal, Somenath; Lal, Siddhartha
2016-01-01
The thermal dynamics of the two-dimensional Ising model and quantum dynamics of the one-dimensional transverse-field Ising model (TFIM) are mapped to one another through the transfer-matrix formalism. We show that the fermionised TFIM undergoes a Fermi-surface topology-changing Lifshitz transition at its critical point. We identify the degree of freedom which tracks the Lifshitz transition via changes in topological quantum numbers (e.g., Chern number, Berry phase etc.). An emergent $SU(2)$ symmetry at criticality is observed to lead to a topological quantum number different from that which characterises the ordered phase. The topological transition is also understood via a spectral flow thought-experiment in a Thouless charge pump, revealing the bulk-boundary correspondence across the transition. The duality property of the phases and their entanglement content are studied, revealing a holographic relation with the entanglement at criticality. The effects of a non-zero longitudinal field and interactions tha...
Multicritical behavior in dissipative Ising models
Overbeck, Vincent R; Gorshkov, Alexey V; Weimer, Hendrik
2016-01-01
We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.
Quantum Ising model coupled with conducting electrons
Energy Technology Data Exchange (ETDEWEB)
Yamashita, Yasufumi; Yonemitsu, Kenji [Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585 (Japan); Graduate University for Advanced studies, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585 (Japan)
2005-01-01
The effect of photo-doping on the quantum paraelectric SrTiO{sub 3} is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.
Quantum Ising model coupled with conducting electrons
Yamashita, Yasufumi; Yonemitsu, Kenji
2005-01-01
The effect of photo-doping on the quantum paraelectric SrTiO3 is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.
Graphical representations of Ising and Potts models
Björnberg, Jakob E
2010-01-01
We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second model is the space-time percolation process, which is closely related to the contact model for the spread of disease. We consider a `space-time' random-cluster model and explore a range of useful probabilistic techniques for studying it. The space-time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated, such as the fact that there is at most one unbounded FK-cluster, and the resulting lower bound on the critical value in $\\ZZ$. We also develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much great...
Duality and conformal twisted boundaries in the Ising model
Grimm, U
2002-01-01
There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper symmetry of the model at criticality. Thus, at criticality, the duality-twisted Ising model is translationally invariant, similar to the more familiar cases of periodic and antiperiodic boundary conditions. The complete finite-size spectrum of the Ising quantum chain with this peculiar boundary condition is obtained.
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.
Classical Ising Models Realised on Optical Lattices
Cirio, Mauro; Brennen, G. K.; Twamley, J.; Iblisdir, S.; Boada, O.
2012-02-01
We describe a simple quantum algorithm acting on a register of qubits in d spatial dimensions which computes statistical properties of d+1 dimensional classical Ising models. The algorithm works by measuring scattering matrix elements for quantum processes and Wick rotating to provide estimates for real partition functions of classical systems. This method can be implemented in a straightforward way in ensembles of qubits, e.g. three dimensional optical lattices with only nearest neighbor Ising like interactions. By measuring noise in the estimate useful information regarding location of critical points and scaling laws can be extracted for classical Ising models, possibly with inhomogeneity. Unlike the case of quantum simulation of quantum hamiltonians, this algorithm does not require Trotter expansion of the evolution operator and thus has the advantage of being amenable to fault tolerant gate design in a straightforward manner. Through this setting it is possible to study the quantum computational complexity of the estimation of a classical partition function for a 2D Ising model with non uniform couplings and magnetic fields. We provide examples for the 2 dimensional case.
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....
Dittrich, Bianca
2013-01-01
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of intertwiner contractions leads to the partition function of the 2d Ising model. This implies that the intertwiner model possesses a second order phase transition, thus leading to a continuum limit with propagating degrees of freedom.
Bond diluted Ising model in 2D
Directory of Open Access Journals (Sweden)
Bouamrane Rachid
2013-03-01
Full Text Available The bond diluted Ising model is studied by Monte Carlo method. The simulation is carried out on a two dimensional square lattice with missing bonds and free boundary conditions. The aim of this work is to investigate the thermodynamical properties of this model for different disorder degree parameter σ. The critical temperature is determined from the Binder cumulant and is shown to decreases as the disorder parameter σ increases linearly.
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Chertkov, Michael [Los Alamos National Laboratory; Netrapalli, Praneeth [STUDENT UT AUSTIN
2010-11-12
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We present the results of numerical experiments evaluating the performance of our algorithm.
Complexity of Ising Polynomials
Kotek, Tomer
2011-01-01
This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and external field. One may consider such an Ising system as a simple graph together with vertex and edge weight values. When these weights are considered indeterminates, the partition function for the constant case is a trivariate polynomial Z(G;x,y,z). This polynomial was studied with respect to its approximability by L. A. Goldberg, M. Jerrum and M. Patersonin 2003. Z(G;x,y,z) generalizes a bivariate polynomial Z(G;t,y), which was studied in by D. Andr\\'{e}n and K. Markstr\\"{o}m in 2009. We consider the complexity of Z(G;t,y) and Z(G;x,y,z) in comparison to that of the Tutte polynomial, which is well-known to be closely related to the Potts model in the absence of an external field. We show that Z(G;\\x,\\y,\\z) is #P-hard to evaluate at all points in $mathbb{Q}^3$, except those in ...
ISE System Development Methodology Manual
Energy Technology Data Exchange (ETDEWEB)
Hayhoe, G.F.
1992-02-17
The Information Systems Engineering (ISE) System Development Methodology Manual (SDM) is a framework of life cycle management guidelines that provide ISE personnel with direction, organization, consistency, and improved communication when developing and maintaining systems. These guide-lines were designed to allow ISE to build and deliver Total Quality products, and to meet the goals and requirements of the US Department of Energy (DOE), Westinghouse Savannah River Company, and Westinghouse Electric Corporation.
Integrated Support Environment (ISE) Laboratory
Federal Laboratory Consortium — Purpose:The Integrated Support Environment (ISE) Laboratory serves the fleet, in-service engineers, logisticians and program management offices by automatically and...
Integrated Support Environment (ISE) Laboratory
Federal Laboratory Consortium — Purpose: The Integrated Support Environment (ISE) Laboratory serves the fleet, in-service engineers, logisticians and program management offices by automatically and...
Frustration in Vicinity of Transition Point of Ising Spin Glasses
Miyazaki, Ryoji
2013-09-01
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lattices, hierarchical lattices, and three-body Ising spin glasses with binary couplings on two-dimensional lattices. In addition, the same argument in the Sherrington--Kirkpatrick model yields a point that is identical to the replica-symmetric solution of the transition point at zero temperature.
Hystad, Grethe
2010-01-01
In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum of the transfer matrix for the finite periodic Ising model. We then determine formulas for the spin correlation functions that depend on the matrix elements of the induced rotation associated with the spin operator in a basis of eigenvectors for the transfer matrix. The representation of the spin matrix elements is obtained by considering the spin operator as an intertwining map. We exhibit the "new" elements V+ and V- in the Bugrij-Lisovyy formula as part of a holomorphic factorization of the periodic and anti-periodic summability kernels on the spectral curve associated with the induced rotation for the transfer matrix.
Spectrum of a duality-twisted Ising quantum chain
Grimm, U
2002-01-01
The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.
Fermions as generalized Ising models
Wetterich, C.
2017-04-01
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.
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
On scaling properties of cluster distributions in Ising models
Ruge, C.; Wagner, F.
1992-01-01
Scaling relations of cluster distributions for the Wolff algorithm are derived. We found them to be well satisfied for the Ising model in d=3 dimensions. Using scaling and a parametrization of the cluster distribution, we determine the critical exponent β/ν=0.516(6) with moderate effort in computing time.
Large Scale Simulations of the Kinetic Ising Model
Münkel, Christian
We present Monte Carlo simulation results for the dynamical critical exponent z of the two- and three-dimensional kinetic Ising model. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems with up to (169984)2 and (3072)3 spins. To our knowledge, these are the largest Ising-systems simulated todate. We also report the successful simulation of very large lattices on a massively parallel MIMD computer with high speedups of approximately 1000 and an efficiency of about 0.93.
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.
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.
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.
Directory of Open Access Journals (Sweden)
Z Jalali mola
2011-12-01
Full Text Available The Ising model is one of the simplest models describing the interacting particles. In this work, we calculate the high temperature series expansions of zero field susceptibility of ising model with ferromagnetic, antiferromagnetic and one antiferromagnetic interactions on two dimensional kagome lattice. Using the Pade´ approximation, we calculate the susceptibility of critical exponent of ferromagnetic ising model γ ≈ 1.75, which is consistent with universality hypothesis. However, antiferromagnetic and one antiferromagnetic interaction ising model doesn’t show any transition at finite temperature because of the effect of magnetic frustration.
Highly Nonlinear Ising Model and Social Segregation
Sumour, M A; Shabat, M M
2011-01-01
The usual interaction energy of the random field Ising model in statistical physics is modified by complementing the random field by added to the energy of the usual Ising model a nonlinear term S^n were S is the sum of the neighbor spins, and n=0,1,3,5,7,9,11. Within the Schelling model of urban segregation, this modification corresponds to housing prices depending on the immediate neighborhood. Simulations at different temperatures, lattice size, magnetic field, number of neighbors and different time intervals showed that results for all n are similar, expect for n=3 in violation of the universality principle and the law of corresponding states. In order to find the critical temperatures, for large n we no longer start with all spins parallel but instead with a random configuration, in order to facilitate spin flips. However, in all cases we have a Curie temperature with phase separation or long-range segregation only below this Curie temperature, and it is approximated by a simple formula: Tc is proportion...
Nonequilibrium antiferromagnetic mixed-spin Ising model.
Godoy, Mauricio; Figueiredo, Wagner
2002-09-01
We studied an antiferromagnetic mixed-spin Ising model on the square lattice subject to two competing stochastic processes. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip (Glauber dynamics). Besides, the system interacts with an external agency of energy, which supplies energy to it whenever two nearest neighboring spins are simultaneously flipped. By employing Monte Carlo simulations and a dynamical pair approximation, we found the phase diagram for the stationary states of the model in the plane temperature T versus the competition parameter between one- and two-spin flips p. We observed the appearance of three distinct phases, that are separated by continuous transition lines. We also determined the static critical exponents along these lines and we showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.
Quantum dimensions from local operator excitations in the Ising model
Caputa, Pawel
2016-01-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Renyi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as t...
Strecka, Jozef; Canová, Lucia; Minami, Kazuhiko
2009-05-01
The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.
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.
Thin Ising films with competing walls: A Monte Carlo study
Binder, K.; Landau, D. P.; Ferrenberg, A. M.
1995-04-01
Ising magnets with a nearest neighbor ferromagnetic exchange interaction J on a simple cubic lattice are studied in a thin film geometry using extensive Monte Carlo simulations. The system has two large L×L parallel free surfaces, a distance D apart from each other, at which competing surface fields act, i.e., HD=-H1. In this geometry, the phase transition occurring in the bulk at a temperature Tcb is suppressed, and instead one observes the gradual formation of an interface between coexisting phases stabilized by the surface fields. While this interface is located in the center of the film for temperatures Tc(D)interface localization-delocalization transition predicted by Parry and Evans [Phys. Rev. Lett. 64, 439 (1990); Physica A 181, 250 (1992)]. For Tinterface is located either close to the left wall where H10 (and the total magnetization is negative). As predicted, for large D this transition temperature Tc(D) is close to the wetting transition Tw(H1) of the semi-infinite system, but the transition nevertheless has a two-dimensional Ising character. Due to crossover problems (for D-->∞ the width of the asymptotic Ising region shrinks to zero, and one presumably observes critical wetting in this model) this Ising nature is clearly seen only for rather thin films. For Tc(D)
Universality class of the two-dimensional site-diluted Ising model.
Martins, P H L; Plascak, J A
2007-07-01
In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70universality class of the diluted Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.
Ising exponents from the functional renormalisation group
Litim, Daniel F
2010-01-01
We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross-correlations of scaling exponents, and their dependence on dimensionality. We find a very good numerical convergence of the derivative expansion, also in comparison with earlier findings. Evaluating the data from all functional renormalisation group studies to date, we estimate the systematic error which is found to be small and in good agreement with findings from Monte Carlo simulations, \\epsilon-expansion techniques, and resummed perturbation theory.
The quantum Ising model: finite sums and hyperbolic functions
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
Bogdan Damski
2015-01-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn...
Rosaria Marraffino
2014-01-01
CRISTAL-ISE, a new version of the CRISTAL data tracking software developed at CERN in the late 90s, has recently been launched under an open source license. The potential for applications of this free software outside particle physics covers several areas, including medicine, where CRISTAL-ISE helps to monitor the progress of Alzheimer’s Disease. CMS lead tungstate crystals produced in Russia. CRISTAL began as a collaboration between CERN, the University of the West of England (UWE) and the Centre National de la Recherche Scientifique (CNRS).“At the time of CMS’s construction, there was a need for software able to track the production of the almost 80,000 lead tungstate crystals for the Electromagnetic Calorimeter,” explains Andrew Branson, member of the CMS collaboration and Technical Coordinator of the CRISTAL-ISE project. “We started to develop the software when we didn’t yet know the detector testing procedures to go through,...
Cluster dynamics and universality of Ising lattice gases
Heringa, J. R.; Blöte, H. W. J.
Lattice gases with nearest-neighbour exclusion are studied by means of Monte Carlo simulations with an efficient cluster algorithm. The critical dynamics is consistent with a dynamical exponent z=0 in the case of Wolff-like cluster updates for square and simple-cubic lattices in the studied range of lattice sizes. We find the critical activity zc=0.72020(4) for the body-centred cubic lattice. The critical exponents yh=2.475(8) and yt=1.61(6) disagree with an earlier study, but they do agree with the known values for the three-dimensional Ising universality class.
Overlap distribution of the three-dimensional Ising model.
Berg, Bernd A; Billoire, Alain; Janke, Wolfhard
2002-10-01
We study the Parisi overlap probability density P(L)(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point, P(L)(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multioverlap MC algorithm. Below the critical temperature, interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.
Ising-like patterns of spatial synchrony in population biology
Noble, Andrew; Hastings, Alan; Machta, Jon
2014-03-01
Systems of coupled dynamical oscillators can undergo a phase transition between synchronous and asynchronous phases. In the case of coupled map lattices, the spontaneous symmetry breaking of a temporal-phase order parameter is known to exhibit Ising-like critical behavior. Here, we investigate a noisy coupled map motivated by the study of spatial synchrony in ecological populations far from the extinction threshold. Ising-like patterns of criticality, as well as spinodal decomposition and homogeneous nucleation, emerge from the nonlinear interactions of environmental fluctuations in habitat quality, local density-dependence in reproduction, and dispersal. In the mean-field limit, the correspondence to the Ising model is exact: the fixed points of our dynamical system are given by the equation of state for Weiss mean-field theory under an appropriate mapping of parameters. We have strong evidence that a quantitative correspondence persists, both near and far from the critical point, in the presence of fluctuations. Our results provide a formal connection between equilibrium statistical physics and population biology. This work is supported by the National Science Foundation under Grant No. 1344187.
Institute of Scientific and Technical Information of China (English)
何春山; 李志兵
2003-01-01
The correlation function of a two-dimensionalIsing model is calculated by the corner transfer matrix renormalization group method.We obtain the critical exponent η= 0.2496 with few computer resources.
Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models
Si, Lisha; Liao, Xiaoyun; Zhou, Nengji
2016-12-01
With the developed "extended Monte Carlo" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L = 8912, significantly refining the results in earlier literature. In the strong-disorder regime, a new universality class of the Ising-type lattice model is unveiled with the exponents β = 0.304(5) , ν = 1.32(3) , z = 1.12(1) , and ζ = 0.90(1) , quite different from that of the quenched Edwards-Wilkinson equation.
Kinetic properties of small one-dimensional Ising magnetic
Udodov, Vladimir; Spirin, Dmitriy; Katanov Khakas State University Team
2011-03-01
Within the framework of a generalized Ising model, a one-dimensional magnetic of a finite length with free ends is considered. The correlation length critical exponent ν and kinetic critical exponent z of the magnet is calculated taking into account the next nearest neighbor interactions and the external field. Of special interest are non-equilibrium processes taking place within the critical temperature interval, which are characterized critical exponent y and dynamic critical index z . Due to significant difficulties encountered in the experimental investigations (e.g., measurement of z) , a natural solution to this complex problem would be modeling of those non-eqilibrium processes. This work addresses non-equilibrium processes in one-dimensional magnetics. Using the Monte Carlo method, an equilibrium critical exponent of the correlation length ν and the dynamic critical index z are calculated for a finite-size magnetic.
A MATLAB GUI to study Ising model phase transition
Thornton, Curtislee; Datta, Trinanjan
We have created a MATLAB based graphical user interface (GUI) that simulates the single spin flip Metropolis Monte Carlo algorithm. The GUI has the capability to study temperature and external magnetic field dependence of magnetization, susceptibility, and equilibration behavior of the nearest-neighbor square lattice Ising model. Since the Ising model is a canonical system to study phase transition, the GUI can be used both for teaching and research purposes. The presence of a Monte Carlo code in a GUI format allows easy visualization of the simulation in real time and provides an attractive way to teach the concept of thermal phase transition and critical phenomena. We will also discuss the GUI implementation to study phase transition in a classical spin ice model on the pyrochlore lattice.
Creep motion in a random-field Ising model.
Roters, L; Lübeck, S; Usadel, K D
2001-02-01
We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.
Krapivsky, P. L.; Mallick, Kirone; Sadhu, Tridib
2015-01-01
We consider an Ising ferromagnet endowed with zero-temperature spin-flip dynamics and examine the evolution of the Ising quadrant, namely the spin configuration when the minority phase initially occupies one quadrant while the majority phase occupies the three remaining quadrants. The two phases are then always separated by a single interface, which generically recedes into the minority phase in a self-similar diffusive manner. The area of the invaded region grows (on average) linearly with time and exhibits non-trivial fluctuations. We map the interface separating the two phases onto the one-dimensional symmetric simple exclusion process and utilize this isomorphism to compute basic cumulants of the area. First, we determine the variance via an exact microscopic analysis (the Bethe ansatz). Then we turn to a continuum treatment by recasting the underlying exclusion process into the framework of the macroscopic fluctuation theory. This provides a systematic way of analyzing the statistics of the invaded area and allows us to determine the asymptotic behaviors of the first four cumulants of the area.
Energy Technology Data Exchange (ETDEWEB)
Ayuela, A. [Donostia International Physics Center (DIPC), P.O. Box 1072, 20018 San Sebastian/Donostia (Spain)]. E-mail: swxayfea@sw.ehu.es; Klein, D.J. [Department of Marine Science, Texas A and M University at Galveston, Galveston, TX 77553 (United States); March, N.H. [Donostia International Physics Center (DIPC), P.O. Box 1072, 20018 San Sebastian/Donostia (Spain) and Oxford University, Oxford (United Kingdom)]. E-mail: arubio@sc.ehu.es
2007-03-12
The critical line of an Ising antiferromagnet (AF) with short-range exchange interactions has been discussed fairly recently by Wang and Kim. Their results may prove appropriate to some insulating AFs. Here, because of possible relevance to metallic AFs such as FeNiCr alloys, we study the Ising model in the opposite limit in which the exchange interactions become infinite range. In particular, we present numerical results for the sublattice magnetizations m{sub A} and m{sub B} as a function of the temperature and applied field. Then, using the so-called smoothness postulate, the critical line of an AF with infinite-range interactions is obtained.
Gauge model with Ising vacancies: Multicritical behavior of self-avoiding surfaces
Maritan, A.; Seno, F.; Stella, A. L.
1991-08-01
A openZ2 gauge model with n-component-vector degrees of freedom on a dodecahedral lattice is coupled to an Ising system on the dual lattice. The statistics of interacting self-avoiding surfaces (SAS) is obtained in the n-->0 limit. At the percolative critical point an exact identification of the SAS critical behavior with that of Ising cluster hulls holds. This condition corresponds to a multicritical point for SAS, in universality class different from that of branched polymers. The model allows application of standard statistical methods to SAS. A mean-field calculation gives a phase diagram remarkably consistent with the above results.
One-dimensional Ising model with multispin interactions
Turban, L
2016-01-01
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 (BC) 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 (1D) 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 $m\\times N/m$, has the topology of a cylinder with helical BC. In the thermodynamic limit $N/m\\to\\infty$, $m\\to\\infty$, a 2D critical singularity develops on the self-duality line, $\\sinh 2K\\sinh 2H=1$.
Stable Degeneracies for Ising Models
Knauf, Andreas
2016-10-01
We introduce and consider the notion of stable degeneracies of translation invariant energy functions, taken at spin configurations of a finite Ising model. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction. We show that besides the symmetry-induced degeneracies, related to spin flip, translation and reflection, there exist additional stable degeneracies, due to more subtle symmetries. One such symmetry is the one of the Singer group of a finite projective plane. Others are described by combinatorial relations akin to trace identities. Our results resemble traits of the length spectrum for closed geodesics on a Riemannian surface of constant negative curvature. There, stable degeneracy is defined w.r.t. Teichmüller space as parameter space.
DEFF Research Database (Denmark)
Roudi, Yasser; Tyrcha, Joanna; Hertz, John
2009-01-01
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......(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...... 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...
Ising model for distribution networks
Hooyberghs, H; Giuraniuc, C; Van Schaeybroeck, B; Indekeu, J O
2012-01-01
An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of t...
The Ising model as a pedagogical tool
Smith, Ryan; Hart, Gus L. W.
2010-10-01
Though originally developed to analyze ferromagnetic systems, the Ising model also provides an excellent framework for modeling alloys. The original Ising model represented magnetic moments (up or down) by a +1 or -1 at each point on a lattice and allowed only nearest neighbors interactions to be non-zero. In alloy modeling, the values ±1 represent A and B atoms. The Ising Hamiltonian can be used in a Monte Carlo approach to simulate the thermodynamics of the system (e.g., an order-disorder transition occuring as the temperature is lowered). The simplicity of the model makes it an ideal starting point for a qualitative understanding of magnetism or configuration ordering in a metal. I will demonstrate the application of the Ising model in simple, two-dimensional ferromagnetic systems and alloys.
Ising Model on an Infinite Ladder Lattice
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.
International Sun-Earth Explorer (ISEE)
Murdin, P.
2000-11-01
Series of three US satellites designed to study the solar wind and its interaction with the Earth's magnetosphere. ISEE-1 and 2 were placed into highly elliptical Earth orbits. ISEE-3 was placed in a halo orbit at the L1 Lagrangian point between the Sun and Earth. It gave advance warning of solar storms heading towards Earth. (See also INTERNATIONAL COMETARY EXPLORER and EXPLORER.)...
Chinese Scholars Attended ISEE 2008 NAIROBI
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
@@ The 10th Biennial International Society for Ecological Economics Conferece was held on Aug.7-11,2008 in Nairobi,the Capital of Kenya.The conference,"ISEE2008 NAIROBI:Applying Ecological Economics for Social and Environmental Sustainability"was a joint undertaking by the International Society for Eclological Economics(ISEE),Afroican Society for Ecological Economics (ASEE)and the United Nations Environment Programme(UNEP).
Ising formulations of many NP problems
Lucas, Andrew
2014-02-01
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.
Harmonic measure for percolation and ising clusters including rare events.
Adams, David A; Sander, Leonard M; Ziff, Robert M
2008-10-03
We obtain the harmonic measure of the hulls of critical percolation clusters and Ising-model Fortuin-Kastelyn clusters using a biased random-walk sampling technique which allows us to measure probabilities as small as 10{-300}. We find the multifractal D(q) spectrum including regions of small and negative q. Our results for external hulls agree with Duplantier's theoretical predictions for D(q) and his exponent -23/24 for the harmonic measure probability distribution for percolation. For the complete hull, we find the probability decays with an exponent of -1 for both systems.
Quantum dimensions from local operator excitations in the Ising model
Caputa, Paweł; Rams, Marek M.
2017-02-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.
On the diagonal susceptibility of the two-dimensional Ising model
Energy Technology Data Exchange (ETDEWEB)
Tracy, Craig A. [Department of Mathematics, University of California, Davis, California 95616 (United States); Widom, Harold [Department of Mathematics, University of California, Santa Cruz, California 95064 (United States)
2013-12-15
We consider the diagonal susceptibility of the isotropic 2D Ising model for temperatures below the critical temperature. For a parameter k related to temperature and the interaction constant, we extend the diagonal susceptibility to complex k inside the unit disc, and prove the conjecture that the unit circle is a natural boundary.
Multiple Ising models coupled to 2-d gravity: a CSD analysis
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-04-01
We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.
Condensation of handles in the interface of 3D Ising model
Caselle, M.; Gliozzi, F.; Vinti, S.
1993-01-01
We analyze the microscopic, topological structure of the interface between domains of opposite magnetization in 3D Ising model near the critical point. This interface exhibits a fractal behaviour with a high density of handles. The mean area is an almost linear function of the genus. The entropy exponent is affected by strong finite-size effects.
Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
Malakis, A.; Gulpinar, G.; Karaaslan, Y.; Papakonstantinou, T.; Aslan, G.
2012-03-01
The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.
Finite size scaling analysis of intermittency moments in the two dimensional Ising model
Burda, Z; Peschanski, R; Wosiek, J
1993-01-01
Finite size scaling is shown to work very well for the block variables used in intermittency studies on a 2-d Ising lattice. The intermittency exponents so derived exhibit the expected relations to the magnetic critical exponent of the model. Email contact: pesch@amoco.saclay.cea.fr
Ron, Dorit; Brandt, Achi; Swendsen, Robert H
2017-05-01
We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.
Empirical relations between static and dynamic exponents for Ising model cluster algorithms
Coddington, Paul D.; Baillie, Clive F.
1992-02-01
We have measured the autocorrelations for the Swendsen-Wang and the Wolff cluster update algorithms for the Ising model in two, three, and four dimensions. The data for the Wolff algorithm suggest that the autocorrelations are linearly related to the specific heat, in which case the dynamic critical exponent is zint,EW=α/ν. For the Swendsen-Wang algorithm, scaling the autocorrelations by the average maximum cluster size gives either a constant or a logarithm, which implies that zint,ESW=β/ν for the Ising model.
Empirical relations between static and dynamic exponents for Ising model cluster algorithms
Energy Technology Data Exchange (ETDEWEB)
Coddington, P.D. (Department of Physics, Syracuse University, Syracuse, New York 13244 (United States)); Baillie, C.F. (Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States))
1992-02-17
We have measured the autocorrelations for the Swendsen-Wang and the Wolff cluster update algorithms for the Ising model in two, three, and four dimensions. The data for the Wolff algorithm suggest that the autocorrelations are linearly related to the specific heat, in which case the dynamic critical exponent is {ital z}{sub int,}{ital E}{sup W}={alpha}/{nu}. For the Swendsen-Wang algorithm, scaling the autocorrelations by the average maximum cluster size gives either a constant or a logarithm, which implies that {ital z}{sub int,}{ital E}{sup SW}={beta}/{nu} for the Ising model.
GPU-based single-cluster algorithm for the simulation of the Ising model
Komura, Yukihiro; Okabe, Yutaka
2012-02-01
We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.
GPU-based single-cluster algorithm for the simulation of the Ising model
Komura, Yukihiro
2011-01-01
We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L=4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L=256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.
Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
Fytas, N. G.; Malakis, A.; Hadjiagapiou, I. A.
2008-11-01
We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied, and their general universality aspects are inspected by means of a detailed finite size scaling (FSS) analysis. We find that the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties as regards a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. However, a careful FSS analysis of our data favors the field theoretically predicted logarithmic corrections.
The scaling limit of the energy correlations in non integrable Ising models
Giuliani, Alessandro; Mastropietro, Vieri
2012-01-01
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\\lambda$, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in $\\lambda$. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit...
Properties of the Ising magnet confined in a corner geometry
Albano, Ezequiel V.; de Virgiliis, Andres; Müller, Marcus; Binder, Kurt
2007-10-01
The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature T of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T(h) runs from the upper left corner to the lower right corner, while for Tinterface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T(h) it scales as w∝√{L}. The distribution P(ℓ) of the interface position ℓ (measured along the z-direction from the corners) decays exponentially for TT(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.
The hobbyhorse of magnetic systems: the Ising model
Ibarra-García-Padilla, Eduardo; Gerardo Malanche-Flores, Carlos; Poveda-Cuevas, Freddy Jackson
2016-11-01
In undergraduate statistical mechanics courses the Ising model always plays an important role because it is the simplest non-trivial model used to describe magnetic systems. The one-dimensional model is easily solved analytically, while the two-dimensional one can be solved exactly by the Onsager solution. For this reason, numerical simulations are usually used to solve the two-dimensional model. Keeping in mind that the two-dimensional model is the platform for studying phase transitions, it is usually an exercise in computational undergraduate courses because its numerical solution is relatively simple to implement and its critical exponents are perfectly known. The purpose of this article is to present a detailed numerical study of the second-order phase transition in the two-dimensional Ising model at an undergraduate level, allowing readers not only to compare the mean-field solution, the exact solution and the numerical one through a complete study of the order parameter, the correlation function and finite-size scaling, but to present the techniques, along with hints and tips, for solving it themselves. We present the elementary theory of phase transitions and explain how to implement Markov chain Monte Carlo simulations and perform them for different lattice sizes with periodic boundary conditions. Energy, magnetization, specific heat, magnetic susceptibility and the correlation function are calculated and the critical exponents determined by finite-size scaling techniques. The importance of the correlation length as the relevant parameter in phase transitions is emphasized.
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.
Interfaces in Random Field Ising Systems
Seppälä, Eira
2001-03-01
Domain walls are studied in random field Ising magnets at T=0 in two and three dimensions using exact ground state calculations. In 2D below the random field strength dependent length scale Lb the walls exhibit a super-rough behavior with a roughness exponent greater than unity ζ ~= 1.20 ± 0.05. The nearest-neighbor height difference probability distribution depends on the system size below L_b. Above Lb domains become fractal, ζ ~= 1.(E. T. Seppälä, V. Petäjä, and M. J. Alava, Phys. Rev. E 58), R5217 (1998). The energy fluctuation exponent has a value θ=1, contradicting the exponent relation θ = 2ζ -1 due to the broken scale-invariance, below Lb and vanishes for system sizes above L_b. The broken scale-invariance should be manifest also in Kardar-Parisi-Zhang problem with random-field noise.(E. Frey, U. C. Täuber, and H. K. Janssen, Europhys. Lett. 47), 14 (1999). In 3D there exists a transition between ferromagnetic and paramagnetic phases at the critical random field strength (Δ/J)_c. Below (Δ/J)c the roughness exponent is also greater ζ ~= 0.73 ± 0.03 than the functional-renormalization-group calculation result ζ = (5-d)/3.(D. Fisher, Phys. Rev. Lett. 56), 1964 (1986).(P. Chauve, P. Le Doussal, and K. Wiese, cond-mat/0006056.) The height differences are system size dependent in 3D, as well. The behavior of the domain walls in 2D below Lb with a constant external field, i.e., the random-bulk wetting, is demonstrated.(E. T. Seppälä, I. Sillanpää, and M. J. Alava, unpublished.)
Observation of Schramm-Loewner evolution on the geometrical clusters of the Ising model
Najafi, M. N.
2015-05-01
Schramm-Loewner Evolution (SLE) is a stochastic process that, by focusing on the geometrical features of the two-dimensional (2D) conformal invariant models, classifies them using one real parameter κ. In this work we apply the SLE formalism to the exterior frontiers of the geometrical clusters (interfaces) of the two-dimensional critical Ising model on the triangular lattice. We first analyze the critical curves going from the real axis to the real axis in the upper half plane geometry and show numerically that SLE(κ, κ - 6) works well to extract the diffusivity parameter κ. We then analyze the conformal loops of the critical Ising model. After determining some geometrical exponents of the critical loops as the interfaces of the model in hand, we address the problem of application of SLE to conformal loops. We numerically show that SLE(κ, κ - 6) is more reliable than previous methods.
Complex-temperature singularities of Ising models
Shrock, R E
1995-01-01
We report new results on complex-temperature properties of Ising models. These include studies of the s=1/2 model on triangular, honeycomb, kagom\\'e, 3 \\cdot 12^2, and 4 \\cdot 8^2 lattices. We elucidate the complex--T phase diagrams of the higher-spin 2D Ising models, using calculations of partition function zeros. Finally, we investigate the 2D Ising model in an external magnetic field, mapping the complex--T phase diagram and exploring various singularities therein. For the case \\beta H=i\\pi/2, we give exact results on the phase diagram and obtain susceptibility exponents \\gamma' at various singularities from low-temperature series analyses.
ISEES: an institute for sustainable software to accelerate environmental science
Jones, M. B.; Schildhauer, M.; Fox, P. A.
2013-12-01
Software is essential to the full science lifecycle, spanning data acquisition, processing, quality assessment, data integration, analysis, modeling, and visualization. Software runs our meteorological sensor systems, our data loggers, and our ocean gliders. Every aspect of science is impacted by, and improved by, software. Scientific advances ranging from modeling climate change to the sequencing of the human genome have been rendered possible in the last few decades due to the massive improvements in the capabilities of computers to process data through software. This pivotal role of software in science is broadly acknowledged, while simultaneously being systematically undervalued through minimal investments in maintenance and innovation. As a community, we need to embrace the creation, use, and maintenance of software within science, and address problems such as code complexity, openness,reproducibility, and accessibility. We also need to fully develop new skills and practices in software engineering as a core competency in our earth science disciplines, starting with undergraduate and graduate education and extending into university and agency professional positions. The Institute for Sustainable Earth and Environmental Software (ISEES) is being envisioned as a community-driven activity that can facilitate and galvanize activites around scientific software in an analogous way to synthesis centers such as NCEAS and NESCent that have stimulated massive advances in ecology and evolution. We will describe the results of six workshops (Science Drivers, Software Lifecycles, Software Components, Workforce Development and Training, Sustainability and Governance, and Community Engagement) that have been held in 2013 to envision such an institute. We will present community recommendations from these workshops and our strategic vision for how ISEES will address the technical issues in the software lifecycle, sustainability of the whole software ecosystem, and the critical
Aneesur Rahman Prize: The Inverse Ising Problem
Swendsen, Robert
2014-03-01
Many methods are available for carrying out computer simulations of a model Hamiltonian to obtain thermodynamic information by generating a set of configurations. The inverse problem consists of recreating the parameters of the Hamiltonian, given a set of configurations. The problem arises in a variety of contexts, and there has been much interest recently in the inverse Ising problem, in which the configurations consist of Ising spins. I will discuss an efficient method for solving the problem and what it can tell us about the Sherrington-Kirkpatrick model.
The Romance of the Ising Model
McCoy, Barry M
2011-01-01
The essence of romance is mystery. In this talk, given in honor of the 60th birthday of Michio Jimbo, I will explore the meaning of this for the Ising model beginning in 1946 with Bruria Kaufman and Willis Lamb, continuing with the wedding by Jimbo and Miwa in 1980 of the Ising model with the Painlev{\\'e} VI equation which had been first discovered by Picard in 1889. I will conclude with the current fascination of the magnetic susceptibility and explore some of the mysteries still outstanding.
Spin-1 Ising model on tetrahedron recursive lattices: Exact results
Jurčišinová, E.; Jurčišin, M.
2016-11-01
We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z = 6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.
Antiferromagnetic Ising model in an imaginary magnetic field
Azcoiti, Vicente; Di Carlo, Giuseppe; Follana, Eduardo; Royo-Amondarain, Eduardo
2017-09-01
We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual θ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multiprecision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line.
Ising model with short-range correlated dilution
Branco, N. S.; de Queiroz, S. L. A.; Dos Santos, Raimundo R.
1988-07-01
We consider a diluted Ising model in which the absence of a spin affects the exchange coupling of a nearest-neighbor pair along the line joining the three spins; that is, it aquires the value αJ, where α is a phenomenological parameter ɛ[0,1]. This model has been proposed to explain the experimental phase diagram for KNixMg1-xF3. A position-space renormalization-group analysis clearly distinguishes two percolation thresholds depending on whether α=0 or α>0, though both cases seem to be in the same universality class. Further, thermal fluctuations dominate over the geometrical ones as in the uncorrelated case and the critical curve (critical temperature versus concentration of magnetic sites) displays an upward curvature for intermediate degrees of correlation 0<α<1, as experimentally observed.
Energy fluctuations and the singularity of specific heat in a 3D Ising model
Kaupuzs, Jevgenijs
2004-05-01
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat Cv based on the finite-size scaling of its maximal values Cvmax depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of Cv. The simulations made up to L Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of Cvmax in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L ɛ [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures t >= 0.000086 and system sizes L <= 410.
Full reduction of large finite random Ising systems by real space renormalization group.
Efrat, Avishay; Schwartz, Moshe
2003-08-01
We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain Gamma(r)=-, the "connected" correlation function, and S(r)=, the "disconnected" correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields, we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the function Gamma(r) along one of the principal axes. (In this work, the full three-dimensional (3D) correlation is calculated and not just parameters such nu or eta). The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.
Generic phase coexistence in the totally asymmetric kinetic Ising model
Godrèche, Claude; Luck, Jean-Marc
2017-07-01
The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question for a specific totally asymmetric kinetic Ising model on the square lattice. This nonequilibrium model possesses the remarkable property that its stationary-state measure in the absence of a magnetic field coincides with that of the usual ferromagnetic Ising model. We use both analytical arguments and numerical simulations in order to make progress in the quantitative understanding of the phenomenon of generic phase coexistence. At zero temperature a mapping onto the TASEP allows an exact determination of the time-dependent shape of the ballistic interface sweeping a large square minority droplet of up or down spins. At finite temperature, measuring the mean lifetime of such a droplet allows an accurate measurement of its shrinking velocity v, which depends on temperature T and magnetic field h. In the absence of a magnetic field, v vanishes with an exponent Δ_v≈2.5+/-0.2 as the critical temperature T c is approached. At fixed temperature in the ordered phase, v vanishes at the phase-boundary fields +/- h_b(T) which mark the limits of the coexistence region. The latter fields vanish with an exponent Δ_h≈3.2+/-0.3 as T c is approached.
Block renormalization study on the nonequilibrium chiral Ising model.
Kim, Mina; Park, Su-Chan; Noh, Jae Dong
2015-01-01
We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any urenormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.
An unusual charging event on ISEE 1
Olsen, R. C.; Whipple, E. C.
1988-06-01
Electrostatic cleanliness requirements on ISEE 1 were expected to prevent negative charging in sunlight. This has largely been true, but on three occasions, ISEE 1 has been observed to charge to significant negative potentials in sunlight. Data from the two electric field experiments and from the plasma composition experiment on ISEE 1 show that the spacecraft charged to close to -70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron spectrometer experiments show that there was a potential barrier of some -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of excess space charge in the plasma. The shape of the barrier suggests that it is due to the former, even though electrostatic cleanliness specifications imposed on ISEE were intended to eliminate differential charging. Modeling of this event showed that the barrier could not be produced by the presence of space charge but that it was most likely produced by differential charging of the solar arrays.
An unusual charging event on ISEE 1
Energy Technology Data Exchange (ETDEWEB)
Olsen, R.C. (Naval Postgraduate School, Monterey, CA (USA)); Whipple, E.C. (Univ. of California at San Diego, La Jolla (USA))
1988-06-01
Electrostatic cleanliness requirements on ISEE 1 were expected to prevent negative charging in sunlight. This has largely been true, but on three occasions, ISEE 1 has been observed to charge to significant negative potentials in sunlight. Data from the two electric field experiments and from the plasma composition experiment on ISEE 1 show that the spacecraft charged to close to {minus}70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of some {minus}10 to {minus}20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of excess space charge in the plasma. The shape of the barrier suggests that it is due to the former, even though electrostatic cleanliness specifications imposed on ISEE were intended to eliminate differential charging. Modeling of this event showed that the barrier could not be produced by the presence of space charge but that it was most likely produced by differential charging of the solar arrays.
Ising, Schelling and Self-Organising Segregation
Stauffer, D
2007-01-01
The similarities between phase separation in physics and residential segregation by preference in the Schelling model of 1971 are reviewed. Also, new computer simulations of asymmetric interactions different from the usual Ising model are presented, showing spontaneous magnetisation (= self-organising segregation) and in one case a sharp phase transition.
Ising, Schelling and self-organising segregation
Stauffer, D.; Solomon, S.
2007-06-01
The similarities between phase separation in physics and residential segregation by preference in the Schelling model of 1971 are reviewed. Also, new computer simulations of asymmetric interactions different from the usual Ising model are presented, showing spontaneous magnetisation (=self-organising segregation) and in one case a sharp phase transition.
Antiferromagnetic Ising model on the swedenborgite lattice
Buhrandt, Stefan; Fritz, Lars
2014-01-01
Geometrical frustration in spin systems often results in a large number of degenerate ground states. In this work, we study the antiferromagnetic Ising model on the three-dimensional swedenborgite lattice, which is a specific stacking of kagome and triangular layers. The model contains two exchange
A novel approach to Ising problems
Hoede, C.; Zandvliet, H.J.W.
2008-01-01
In 2000 Istrail suggested that calculating the partition function of non-planar Ising models is an NP-complete problem, implying that these problems are intractable and thus essentially unsolvable. In this note we discuss the validity of this suggestion and introduce the idea of gauging on an exact
Renyi Correlations and Phase Transitions in the Transverse-Field Ising model
Singh, Rajiv; Devakul, Trithep
2015-03-01
We calculate T = 0 spin-spin correlation functions with respect to a probability distribution given by an integer power (n) of the reduced density matrix ρcirc;A, when a transverse-field Ising model (TFIM) system is bipartitioned by a planar interface. Using series expansion methods these calculations are done in the thermodynamic limit for arbitrary positive integer n, with n = 1 giving us the bulk correlations. We study the TFIM system on isotropic and anisotropic simple-cubic lattices. We examine the evidence for whether the critical point of the transition deviates from the bulk critical point as a function of n and whether the critical behavior lies in the 2 D or 4 D Ising universality classes as would be expected from a surface transition at finite temperature and a T = 0 bulk transition, respectively. Work supported in part by NSF Grant Number DMR-1306048.
RG boundaries and interfaces in Ising field theory
Konechny, Anatoly
2017-04-01
Perturbing a CFT by a relevant operator on a half space and letting the perturbation flow to the far infrared we obtain an RG interface between the UV and IR CFTs. If the IR CFT is trivial we obtain an RG boundary condition. The space of massive perturbations thus breaks up into regions labelled by conformal boundary conditions of the UV fixed point. For the 2D critical Ising model perturbed by a generic relevant operator we find the assignment of RG boundary conditions to all flows. We use some analytic results but mostly rely on TCSA and TFFSA numerical techniques. We investigate real as well as imaginary values of the magnetic field and, in particular, the RG trajectory that ends at the Yang-Lee CFT. We argue that the RG interface in the latter case does not approach a single conformal interface but rather exhibits oscillatory non-convergent behaviour. To the memory of O I Zavialov.
Destroying a topological quantum bit by condensing Ising vortices.
Hao, Zhihao; Inglis, Stephen; Melko, Roger
2014-12-09
The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm.
RG boundaries and interfaces in Ising field theory
Konechny, Anatoly
2016-01-01
Perturbing a CFT by a relevant operator on a half space and letting the perturbation flow to the far infrared we obtain an RG interface between the UV and IR CFTs. If the IR CFT is trivial we obtain an RG boundary condition. The space of massive perturbations thus breaks up into regions labelled by conformal boundary conditions of the UV fixed point. For the 2D critical Ising model perturbed by a generic relevant operator we find the assignment of RG boundary conditions to all flows. We use some analytic results but mostly rely on TCSA and TFFSA numerical techniques. We investigate real as well as imaginary values of the magnetic field and, in particular, the RG trajectory that ends at the Yang-Lee CFT. We argue that the RG interface in the latter case does not approach a single conformal interface but rather exhibits oscillatory non-convergent behaviour.
Critical Behavior of the Widom-Rowlinson Lattice Model
Dickman, R; Dickman, Ronald; Stell, George
1995-01-01
We report extensive Monte Carlo simulations of the Widom-Rowlinson lattice model in two and three dimensions. Our results yield precise values for the critical activities and densities, and clearly place the critical behavior in the Ising universality class.
Ising and Gross-Neveu model in next-to-leading order
Knorr, Benjamin
2016-01-01
We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-$N_f$ calculations, but for a single flavour, different methods disagree quantitatively, and further studies are necessary.
Antiferromagnetic Ising Model in Hierarchical Networks
Cheng, Xiang; Boettcher, Stefan
2015-03-01
The Ising antiferromagnet is a convenient model of glassy dynamics. It can introduce geometric frustrations and may give rise to a spin glass phase and glassy relaxation at low temperatures [ 1 ] . We apply the antiferromagnetic Ising model to 3 hierarchical networks which share features of both small world networks and regular lattices. Their recursive and fixed structures make them suitable for exact renormalization group analysis as well as numerical simulations. We first explore the dynamical behaviors using simulated annealing and discover an extremely slow relaxation at low temperatures. Then we employ the Wang-Landau algorithm to investigate the energy landscape and the corresponding equilibrium behaviors for different system sizes. Besides the Monte Carlo methods, renormalization group [ 2 ] is used to study the equilibrium properties in the thermodynamic limit and to compare with the results from simulated annealing and Wang-Landau sampling. Supported through NSF Grant DMR-1207431.
Classical Ising model test for quantum circuits
Geraci, Joseph; Lidar, Daniel A.
2010-07-01
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.
Phase diagrams of diluted transverse Ising nanowire
Energy Technology Data Exchange (ETDEWEB)
Bouhou, S.; Essaoudi, I. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Ainane, A., E-mail: ainane@pks.mpg.de [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Saber, M. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Ahuja, R. [Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden); Dujardin, F. [Laboratoire de Chimie et Physique des Milieux Complexes (LCPMC), Institut de Chimie, Physique et Matériaux (ICPM), 1 Bd. Arago, 57070 Metz (France)
2013-06-15
In this paper, the phase diagrams of diluted Ising nanowire consisting of core and surface shell coupling by J{sub cs} exchange interaction are studied using the effective field theory with a probability distribution technique, in the presence of transverse fields in the core and in the surface shell. We find a number of characteristic phenomena. In particular, the effect of concentration c of magnetic atoms, the exchange interaction core/shell, the exchange in surface and the transverse fields in core and in surface shell of phase diagrams are investigated. - Highlights: ► We use the EFT to investigate the phase diagrams of Ising transverse nanowire. ► Ferrimagnetic and ferromagnetic cases are investigated. ► The effects of the dilution and the transverse fields in core and shell are studied. ► Behavior of the transition temperature with the exchange interaction is given.
Initial thermal plasma observations from ISEE-1
Baugher, C. R.; Chappell, C. R.; Horwitz, J. L.; Shelley, E. G.; Young, D. T.
1980-09-01
The initial measurements of magnetospheric thermal ions by the Plasma Composition Experiment on ISEE-1 are presented to demonstrate the surprising variety in this plasma population. The data provide evidence that the adiabatic mapping of the high latitude ionosphere to the equatorial plasma trough provides an insufficient description of the origin, transport, and accumulation processes which supply low energy ions to the outer plasmasphere and plasma trough.
Lattice Radial Quantization: 3D Ising
Brower, Richard; Neuberger, Herbert
2012-01-01
Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using this method, we obtain the preliminary estimate eta=0.034(10).
Ising model for a Brownian donkey
Cleuren, B.; Van den Broeck, C.
2001-04-01
We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.
Ising Expansion for the Hubbard Model
Shi, Zhu-Pei; Singh, Rajiv R. P.
1995-01-01
We develop series expansions for the ground state properties of the Hubbard model, by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional (2D) square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility and spin stiffness are calculated as a function of $U/t$, where $U$ is the Coulomb constant and $t$ is the hopping parameter. Magnetic susceptibility data indicate a crossover around $U\\app...
Phase Transition of a Distance-Dependent Ising Model on the Barabasi-Albert Network
Institute of Scientific and Technical Information of China (English)
DAI Jun; HE Da-Ren
2007-01-01
We report our investigation on the behaviour of distance-dependent Ising models,which are located on the BA model network.The interaction strength between two nodes(the spins) is considered to obey an exponential decay dependence on the geometrical distance.The Monte Carlo simulation shows a phase transition from ferromagnetism to paramagnetism,and the critical temperature approaches a constant temperature as the interaction decaying exponent increases.
Ground-state entanglement in a three-spin transverse Ising model with energy current
Institute of Scientific and Technical Information of China (English)
Zhang Yong; Liu Dan; Long Gui-Lu
2007-01-01
The ground-state entanglement associated with a three-spin transverse Ising model is studied. By introducing an energy current into the system, a quantum phase transition to energy-current phase may be presented with the variation of external magnetic field; and the ground-state entanglement varies suddenly at the critical point of quantum phase transition. In our model, the introduction of energy current makes the entanglement between any two qubits become maximally robust.
Puzzo, M. Leticia Rubio; Albano,Ezequiel V.
2007-01-01
The propagation of damage in a confined magnetic Ising film, with short range competing magnetic fields ($h$) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well defined critical temperature $T_w(h)$. In fact, the competing fields causes the occurrence of an interface between magnetic domains of different orientation. For $T T_w(h)$) such interface is bounded (unbounded) ...
The scaling limit of the energy correlations in non integrable Ising models
2012-01-01
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\\lambda$, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis an...
On bimodal size distribution of spin clusters in the one dimensional Ising model
Ivanytskyi, A. I.; Chelnokov, V. O.
2015-01-01
The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $\\beta$ above some "critical value" $\\beta_c$ the found size distribution demonstrates the non-monotonic behavior with the peak corresponding to the size of largest available cluster. In other words, at high values of lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many cluster...
Dynamics of the Random Ising Model with Long-Range Interaction
Institute of Scientific and Technical Information of China (English)
CHEN Yuan; LI Zhi-Bing; FANG Hai; HE Shun-Shan; SITU Shu-Ping
2001-01-01
Critical dynamics of the random Ising model with long-range interaction decaying as r-(d+σ) where d is the dimensionality) is studied by the theoretic renormalization-group approach. The system is released to an evolution within a model A dynamics. Asymptotic scaling laws are studied in a frame of the expansion in = 2σ - d. In dimensions d ＜ 2σ. the dynamic exponent z is calculated to the second order in at the random fixed point.``
Monte Carlo renormalization: the triangular Ising model as a test case.
Guo, Wenan; Blöte, Henk W J; Ren, Zhiming
2005-04-01
We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.
Spin-1 Ising model: exact damage-spreading relations and numerical simulations.
Anjos, A S; Mariz, A M; Nobre, F D; Araujo, I G
2008-09-01
The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin- 12 Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.
Identifying interacting pairs of sites in infinite range Ising models
Galves, Antonio; Takahashi, Daniel Yasumasa
2010-01-01
We consider Ising models (pairwise interaction Gibbs probability measures) in $\\Z^d$ with an infinite range potential. We address the problem of identifying pairs of interacting sites from a finite sample of independent realisations of the Ising model. The sample contains only the values assigned by the Ising model to a finite set of sites in $\\Z^d$. Our main result is an upperbound for the probability with our estimator to misidentify the pairs of interacting sites in this finite set.
Ordering in Two-Dimensional Ising Models with Competing Interactions
2004-01-01
We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular ...
Toward an Ising model of cancer and beyond.
Torquato, Salvatore
2011-02-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Bound states in the 3d Ising model and implications for QCD at finite temperature and density
Caselle, M; Provero, P; Zarembo, K
2002-01-01
We study the spectrum of bound states of the three dimensional Ising model in the (h,beta) plane near the critical point. We show the existence of an unbinding line, defined as the boundary of the region where bound states exist. Numerical evidence suggests that this line coincides with the beta=beta_c axis. When the 3D Ising model is considered as an effective description of hot QCD at finite density, we conjecture the correspondence between the unbinding line and the line that separates the quark-gluon plasma phase from the superconducting phase. The bound states of the Ising model are conjectured to correspond to the diquarks of the latter phase of QCD.
Nuclear and ionic charge distribution experiment on ISEE-1 and ISEE-3
Gloeckler, G.; Ipavich, F. M.; Galvin, A. B.
1987-01-01
The experimental work carried out under this contract is a continuation of that originally performed under Contracts NAS5-20062 and NAS5-26739. The data analyzed are from the Max-Planck Institut/Univ. of Maryland experiment on ISEE-1 and ISEE-3. Each spacecraft experiment consists of a nearly identical set of three sensors (designated the ULECA, ULEWAT, and ULEZEQ sensors) designed to measure the energy spectra and composition of suprathermal and energetic ions over a broad energy range (less than 3 keV/e to more than 20 MeV/nucleon). Since the launch of ISEE's 2 and 3, the MPI/Univ. of Maryland experiments have generally performed as expected except for a partial failure of the ULEWAT sensor on ISEE-1 in August 1978. A number of scientific studies have either been completed, initiated or are at various stages of completion. A brief summary of Primary Results is given, followed by a more detailed summary of the major accomplishments at the Univ. of Maryland.
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.
Non-Ising-like effects in the liquid-vapor transition: Equations of state
Vause, C.; Sak, J.
1980-06-01
A Landau-Ginzburg-Wilson model is derived for a single-component fluid whose particles interact via a two-body potential. The effective Hamiltonian contains both even and odd powers in the order parameter (local fluid density). We study the effect of quintic interactions absent in the Ising model, and characterized by a new exponent φ5, on various singular thermodynamic functions near the critical point. Mean-field, scaling, and renormalization-group (in d=4-ɛ dimensions) theories are used to evaluate the non-Ising effects due to φ5. One of the main results of the asymmetry in this model is that it produces the leading singularity of the liquid-vapor coexistence diameter near the critical point: |t|β-φ5, where β is the usual order-parameter exponent and t is the reduced temp˙erature. The singularity |t|1-α (α being the specific heat exponent) predicted by earlier phenomenological theories is not present in this theory. The problems associated with observing the non-Ising effects are briefly discussed.
Calibration of the ISEE plasma composition experiment
Baugher, C. R.; Olsen, R. C.; Reasoner, D. L.
1986-01-01
The Plasma Composition experiment on the ISEE-1 satellite was designed to measure ions from 1 to 16 amu, at energies from near zero to 16 keV. The two nearly identical flight instruments were calibrated by means of preflight laboratory tests and in-flight data comparisons. This document presents most of the details of those efforts, with special emphasis on the low energy (0 to 100 eV) portion of the instrument response. The analysis of the instrument includes a ray-tracing calculation, which follows an ensemble of test particles through the detector.
Entrepreneurial Leapfrogging in the Context of ISE
DEFF Research Database (Denmark)
Li, Peter
2013-01-01
We know little regarding the underlying contexts and mechanisms for disruptive innovation initiated by the entrepreneurial firms in the emerging economies. Further, there is limited knowledge about the contexts and mechanisms for global latecomers to catch up with and leapfrog global early......-movers. The cross-fertilization between such two research streams provides a great opportunity to shed light on their link toward an interdisciplinary domain of international strategic entrepreneurship (ISE). This article will develop an integrative typology of global innovations as well as a dynamic model...
Dynamical transitions of a driven Ising interface.
Sahai, Manish K; Sengupta, Surajit
2008-03-01
We study the structure of an interface in a three-dimensional Ising system created by an external nonuniform field H(r,t) . H changes sign over a two-dimensional plane of arbitrary orientation. When the field is pulled with velocity v(e) , [i.e., H(r,t)=H(r-v(e)t) ], the interface undergoes several dynamical transitions. For low velocities it is pinned by the field profile and moves along with it, the distribution of local slopes undergoing a series of commensurate-incommensurate transitions. For large v(e) the interface depins and grows with Kardar-Parisi-Zhang exponents.
Characterization of the Dilute Ising Antiferromagnet
Energy Technology Data Exchange (ETDEWEB)
Wiener, T.
2000-09-12
A spin glass is a magnetic ground state in which ferromagnetic and antiferromagnetic exchange interactions compete, thereby creating frustration and a multidegenerate state with no long range order. An Ising system is a system where the spins are constrained to lie parallel or antiparallel to a primary axis. There has been much theoretical interest in the past ten years in the effects of applying a magnetic field transverse to the primary axis in an Ising spin glass at low temperatures and thus study phase transitions at the T=0 limit. The focus of this study is to search for and characterize a new Ising spin glass system. This is accomplished by site diluting yttrium for terbium in the crystalline material TbNi{sub 2}Ge{sub 2}. The first part of this work gives a brief overview of the physics of rare earth magnetism and an overview of experimental characteristics of spin glasses. This is followed by the methodology used to manufacture the large single crystals used in this study, as well as the measurement techniques used. Next, a summary of the results of magnetic measurements on across the dilution series from pure terbium to pure yttrium is presented. This is followed by detailed measurements on particular dilutions which demonstrate spin glass behavior. Pure TbNi{sub 2}Ge{sub 2} is an Ising antiferromagnet with a several distinct metamagnetic states below 17 K. As the terbium is alloyed with yttrium, these magnetic states are weakened in a consistent manner, as is seen in measurements of the transition temperatures and analysis of Curie-Weiss behavior at high temperature. At low concentrations of terbium, below 35%, long range order is no longer present and a spin-glass-like state emerges. This state is studied through various measurements, dc and ac susceptibility, resistivity, and specific heat. This magnetic behavior was then compared to that of other well characterized spin glasses. It is concluded that there is a region of concentration s for which a spin
Another solution of 2D Ising model
Vergeles, S. N.
2009-04-01
The partition function of the Ising model on a two-dimensional regular lattice is calculated by using the matrix representation of a Clifford algebra (the Dirac algebra), with number of generators equal to the number of lattice sites. It is shown that the partition function over all loops in a 2D lattice including self-intersecting ones is the trace of a polynomial in terms of Dirac matrices. The polynomial is an element of the rotation group in the spinor representation. Thus, the partition function is a function of a character on an orthogonal group of a high degree in the spinor representation.
Characterization of the Dilute Ising Antiferromagnet
Energy Technology Data Exchange (ETDEWEB)
Wiener, Timothy [Iowa State Univ., Ames, IA (United States)
2000-09-12
A spin glass is a magnetic ground state in which ferromagnetic and antiferromagnetic exchange interactions compete, thereby creating frustration and a multidegenerate state with no long range order. An Ising system is a system where the spins are constrained to lie parallel or antiparallel to a primary axis. There has been much theoretical interest in the past ten years in the effects of applying a magnetic field transverse to the primary axis in an Ising spin glass at low temperatures and thus study phase transitions at the T=0 limit. The focus of this study is to search for and characterize a new Ising spin glass system. This is accomplished by site diluting yttrium for terbium in the crystalline material TbNi_{2}Ge_{2}. The first part of this work gives a brief overview of the physics of rare earth magnetism and an overview of experimental characteristics of spin glasses. This is followed by the methodology used to manufacture the large single crystals used in this study, as well as the measurement techniques used. Next, a summary of the results of magnetic measurements on across the dilution series from pure terbium to pure yttrium is presented. This is followed by detailed measurements on particular dilutions which demonstrate spin glass behavior. Pure TbNi_{2}Ge_{2} is an Ising antiferromagnet with a several distinct metamagnetic states below 17 K. As the terbium is alloyed with yttrium, these magnetic states are weakened in a consistent manner, as is seen in measurements of the transition temperatures and analysis of Curie-Weiss behavior at high temperature. At low concentrations of terbium, below 35%, long range order is no longer present and a spin-glass-like state emerges. This state is studied through various measurements, dc and ac susceptibility, resistivity, and specific heat. This magnetic behavior was then compared to that of other well characterized spin glasses. It is concluded that there is a region of
Inverse Ising Inference Using All the Data
Aurell, Erik; Ekeberg, Magnus
2012-03-01
We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.
An Ising model for earthquake dynamics
Directory of Open Access Journals (Sweden)
A. Jiménez
2007-01-01
Full Text Available This paper focuses on extracting the information contained in seismic space-time patterns and their dynamics. The Greek catalog recorded from 1901 to 1999 is analyzed. An Ising Cellular Automata representation technique is developed to reconstruct the history of these patterns. We find that there is strong correlation in the region, and that small earthquakes are very important to the stress transfers. Finally, it is demonstrated that this approach is useful for seismic hazard assessment and intermediate-range earthquake forecasting.
Three representations of the Ising model
Kruis, Joost; Maris, Gunter
2016-01-01
Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense. PMID:27698356
Real-space renormalization group for the transverse-field Ising model in two and three dimensions.
Miyazaki, Ryoji; Nishimori, Hidetoshi; Ortiz, Gerardo
2011-05-01
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.
Transient Loschmidt Echo and Orthogonality Catastrophe in highly excited Quantum Ising Spin Chains
Schiro, Marco; Lupo, Carla
We study the response to sudden local perturbations of highly excited Quantum Ising Spin Chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a transient Loschmidt echo. We compute the Echo perturbatively in the case of a weak local quench and study its asymptotics at long times, which contains crucial information about the structure of the highly excited non-equilibrium environment induced by the quench. Our results reveal that the Echo decays exponentially, rather than power law as in the low-energy Orthogonality Catastrophe, a further example of quench-induced decoherence. The emerging decoherence scale is set by the strenght of the local potential and the bulk excitation energy. In addition, the transient evolution features aging behavior at the Ising quantum critical point.
Effective field study of ising model on a double perovskite structure
Ngantso, G. Dimitri; El Amraoui, Y.; Benyoussef, A.; El Kenz, A.
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.
The Worm Process for the Ising Model is Rapidly Mixing
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-09-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
de Mendonça, J. Ricardo G.
2012-01-01
We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We re...
Character of the Phase Transition in Thin Ising Films with Competing Walls
Binder, K.; Landau, D. P.; Ferrenberg, A. M.
1995-01-01
By extensive Monte Carlo simulations of a lattice gas model we have studied the controversial nature of the gas-liquid transition of a fluid confined between two parallel plates that exert competing surface fields. We find that the transition is shifted to a temperature just below the wetting transition of a semi-infinite fluid but belongs to the two-dimensional Ising universality class. In between this new type of critical point and bulk criticality, a response function xmaxnnvarying exponentially with D is observed, 2 lnχmaxnn/D = l-1, where l is a new length characterizing interfaces.
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...
Santos, Jander P.; Sá Barreto, F. C.
2017-10-01
Thermodynamic and magnetic properties of a trilayer nanostructure of hexagonal lattices described by the spin-1/2 Ising model are investigated by the use of the effective-field theory (EFT) with correlations. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat and the critical frontiers were obtained. The critical temperature and the compensation temperature are investigated with a negative interlayer coupling, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors. From the thermal variations of the total magnetization, the six compensation types can be found, i.e., L-, Q-, R-, S-, P-, and N-types.
Two-Dimensional Wang-Landau Sampling of AN Asymmetric Ising Model
Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.
We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang-Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.
Suzuki-Trotter decomposition and renormalization of a transverse-field Ising model in two dimensions
Dudziński, M.; Sznajd, J.
1997-06-01
The combined Suzuki-Trotter decomposition and Niemeijer-van Leuween real-space renormalization-group techniques are used to study the critical properties of a two-dimensional Ising system with a transverse field. The inverse critical temperature as a function of the external field and the temperature dependence of the transverse component of the magnetization are found. It is also shown that any real-space renormalization-group procedure based on the simple generalization of the Niemeijer-van Leeuwen majority rule for one of the components of the total-cell spin does not preserve the symmetry of the quantum spin space.
SL(2,Z)-Invariant Spaces Spanned by Modular Units
Eholzer, W; Eholzer, Wolfgang; Skoruppa, Nils-Peter
1997-01-01
Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q Z_{>=0}[[q
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.
Differential geometry of the space of Ising models
Machta, Benjamin; Chachra, Ricky; Transtrum, Mark; Sethna, James
2012-02-01
We use information geometry to understand the emergence of simple effective theories, using an Ising model perturbed with terms coupling non-nearest-neighbor spins as an example. The Fisher information is a natural metric of distinguishability for a parameterized space of probability distributions, applicable to models in statistical physics. Near critical points both the metric components (four-point susceptibilities) and the scalar curvature diverge with corresponding critical exponents. However, connections to Renormalization Group (RG) ideas have remained elusive. Here, rather than looking at RG flows of parameters, we consider the reparameterization-invariant flow of the manifold itself. To do this we numerically calculate the metric in the original parameters, taking care to use only information available after coarse-graining. We show that under coarse-graining the metric contracts very anisotropically, leading to a ``sloppy'' spectrum with the metric's Eigenvalues spanning many orders of magnitude. Our results give a qualitative explanation for the success of simple models: most directions in parameter space become fundamentally indistinguishable after coarse-graining.
Rubio Puzzo, M. Leticia; Albano, Ezequiel V.
2002-09-01
The propagation of damage in a confined magnetic Ising film, with short-range competing magnetic fields (h) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well-defined critical temperature Tw(h). In fact, the competing fields cause the occurrence of an interface between magnetic domains of different orientations. For TTw(h)] such an interface is bound (unbound) to the walls, while right at Tw(h) the interface is essentially located at the center of the film. It is found that the spatiotemporal spreading of the damage becomes considerably enhanced by the presence of the interface, which acts as a ``catalyst'' of the damage causing an enhancement of the total damaged area. The critical points for damage spreading are evaluated by extrapolation to the thermodynamic limit using a finite-size scaling approach. Furthermore, the wetting transition effectively shifts the location of the damage spreading critical points, as compared with the well-known critical temperature of the order-disorder transition characteristic of the Ising model. Such critical points are found to be placed within the nonwet phase.
The Role of Interfaces in the Propagation of Damage in the Confined Ising Model
Rubio Puzzo, M. Leticia; Albano, Ezequiel V.
2003-04-01
The propagation of damage in a confined magnetic Ising film, with short range competing magnetic fields (h) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well defined critical temperature Tw(h). In fact, the competing fields causes the occurrence of an interface between magnetic domains of different orientation. For T Tw(h)) such interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is essentially located at the center of the film. It is found that the spatio-temporal spreading of the damage becomes considerably enhanced by the presence of the interface, which act as a "catalyst" of the damage causing an enhancement of the total damaged area. The critical points for damage spreading are evaluated by extrapolation to the thermodynamic limit using a finite-size scaling approach. Furthermore, the wetting transition effectively shifts the location of the damage spreading critical points, as compared with the well known critical temperature of the order-disorder transition characteristic of the Ising model. Such a critical points are found to be placed within the non-wet phase.
Institute of Scientific and Technical Information of China (English)
R. Masrour; M. Hamedoun; A. Benyoussef
2012-01-01
In this work,the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Néel temperature and thickness for layers (n =2,3,4,5,6,and bulk (oo)) by means of a mean-field and high temperature series expansion (HTSE) combined with Padé approximant calculations.The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent % veff (mean),ratio of the critical exponents γ/v,and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n =2,3,4,5,6,and bulk (∞).
Loops, Surfaces and Grassmann Representation in Two- and Three-Dimensional Ising Models
Gattringer, C R; Semenoff, Gordon W
1999-01-01
Starting from the known representation of the partition function of the 2- and 3-D Ising models as an integral over Grassmann variables, we perform a hopping expansion of the corresponding Pfaffian. We show that this expansion is an exact, algebraic representation of the loop- and surface expansions (with intrinsic geometry) of the 2- and 3-D Ising models. Such an algebraic calculus is much simpler to deal with than working with the geometrical objects. For the 2-D case we show that the algebra of hopping generators allows a simple algebraic treatment of the geometry factors and counting problems, and as a result we obtain the corrected loop expansion of the free energy. We compute the radius of convergence of this expansion and show that it is determined by the critical temperature. In 3-D the hopping expansion leads to the surface representation of the Ising model in terms of surfaces with intrinsic geometry. Based on a representation of the 3-D model as a product of 2-D models coupled to an auxiliary field...
Multi-GPU Accelerated Multi-Spin Monte Carlo Simulations of the 2D Ising Model
Block, Benjamin; Preis, Tobias; 10.1016/j.cpc.2010.05.005
2010-01-01
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp. Phys. 228, 4468 (2009)] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.
The scaling limit of the energy correlations in non-integrable Ising models
Giuliani, Alessandro; Greenblatt, Rafael L.; Mastropietro, Vieri
2012-09-01
We obtain an explicit expression for the multipoint energy correlations of a non-solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength λ, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis, and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in λ. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit bounds on the speed of convergence to the scaling limit are derived.
Directory of Open Access Journals (Sweden)
Jacob Olufemi Orimaye
2016-01-01
Full Text Available This study investigated butterfly diversity in the protected area (PA and unprotected area (UPA of Ise Forest reserve, Ise Ekiti, Ekiti State, using sweep net along existing trails. Butterfly species seen in the study sites were captured and released after proper identification was made. The results indicated that a total of 837 butterflies were identified in the study sites with 661 species observed in PA and 176 species in UPA. Butterfly species diversity was significantly different (p≤0.05 between PA and UPA. Shannon diversity index was higher in PA (3.59 than UPA (3.27 as against Menhinick’s index, higher in UPA (2.11 than in PA (1.52. Likewise, 10 families of butterflies were recorded in PA and 8 families in UPA. The family with highest species occurrence was Satyridae (17.9% in PA and Lycaenidae in UPA with 20.1%. Butterfly families’ diversity was not significant (p≥0.05 between the two study sites. Ise Forest Reserve recorded approximately 6.6% of all butterflies recorded in West Africa. The findings indicated that mature secondary and regenerated forests supported high butterfly diversity and species richness, while cultivated land and grassland had a negative impact on butterfly community suggesting the negative effect of agricultural activities on the ecosystem.
Transient Loschmidt echo in quenched Ising chains
Lupo, Carla; Schiró, Marco
2016-07-01
We study the response to sudden local perturbations of highly excited quantum Ising spin chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a transient Loschmidt Echo. Its asymptotics at long time differences contain crucial information about the structure of the highly excited nonequilibrium environment induced by the quench. We compute the echo perturbatively for a weak local quench but for arbitrarily large global quench, using a cumulant expansion. Our perturbative results suggest that the echo decays exponentially, rather than power law as in the low-energy orthogonality catastrophe, a further example of quench-induced decoherence already found in the case of quenched Luttinger liquids. The emerging decoherence scale is set by the strength of the local potential and the bulk excitation energy.
Lattice radial quantization: 3D Ising
Energy Technology Data Exchange (ETDEWEB)
Brower, R.C., E-mail: brower@bu.edu [Department of Physics, Boston University, Boston, MA 02215 (United States); Fleming, G.T., E-mail: george.fleming@yale.edu [Department of Physics, Yale University, New Haven, CT 06520 (United States); Neuberger, H., E-mail: neuberg@physics.rutgers.edu [Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855 (United States)
2013-04-25
Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using the integer spacing of the anomalous dimensions of the first two descendants (l=1,2), we obtain an estimate for η=0.034(10). We also observed small deviations from integer spacing for the 3rd descendant, which suggests that a further improvement of our radial lattice action will be required to guarantee conformal symmetry at the Wilson–Fisher fixed point in the continuum limit.
Ising Ferromagnet: Zero-Temperature Dynamic Evolution
Murilo-Castro de Oliveira, P; 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 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.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
Series Expansions for Frustrated Quantum Ising Magnets
Gelfand, M. P.; Priour, D. J.; Sondhi, S. L.
2000-03-01
We have computed the phase diagram of a frustrated Ising ladder in a transverse field via the Wolff Monte Carlo Cluster algorithm and by Pad'e Analysis of a series for the excitation spectrum about the large transverse field limit. A comparison of the two methods suggests that analysis of the perturbation series is a viable method for obtaining the phase diagrams of such systems even in cases, such as this one , where there is no phase transition down to arbitrarily small values of the transverse field. We will also discuss the application of the series technique to two dimensional systems of greater experimental interest, such as on the Kagome lattice which is also believed to realize a cooperative paramagnet at small transverse fields.
Ground states for nonuniform periodic Ising chains
Martínez-Garcilazo, J. P.; Ramírez, C.
2015-04-01
We generalize Morita's works [J. Phys. A 7, 289 (1974), 10.1088/0305-4470/7/2/014; J. Phys. A 7, 1613 (1974), 10.1088/0305-4470/7/13/015] on ground states of Ising chains, for chains with a periodic structure and different spins, to any interaction order. The main assumption is translational invariance. The length of the irreducible blocks is a multiple of the period of the chain. If there is parity invariance, it restricts the length in general only in the diatomic case. There are degenerated states and under certain circumstances there could be nonregular ground states. We illustrate the results and give the ground state diagrams in several cases.
Charged Ising Model of Neutron Star Matter
Hasnaoui, K H O
2012-01-01
Background: The inner crust of a neutron star is believed to consist of Coulomb-frustrated complex structures known as "nuclear pasta" that display interesting and unique low-energy dynamics. Purpose: To elucidate the structure and composition of the neutron-star crust as a function of temperature, density, and proton fraction. Methods: A new lattice-gas model, the "Charged-Ising Model" (CIM), is introduced to simulate the behavior of neutron-star matter. Preliminary Monte Carlo simulations on 30^3 lattices are performed for a variety of temperatures, densities, and proton fractions. Results: Results are obtained for the heat capacity, pair-correlation function, and static structure factor for a variety of conditions appropriate to the inner stellar crust. Conclusions: Although relatively simple, the CIM captures the essence of Coulomb frustration that is required to simulate the subtle dynamics of the inner stellar crust. Moreover, the computationally demanding long-range Coulomb interactions have been pre-c...
A dilogarithmic 3-dimensional Ising tetrahedron
Broadhurst, D J
1999-01-01
In 3 dimensions, the Ising model is in the same universality class as unknown analytical nature. In contrast, all single-scale 4-dimensional tetrahedra were reduced, in hep-th/9803091, to special values of exponentially convergent polylogarithms. Combining dispersion relations with the integer-relation finder PSLQ, we find that $C^{Tet}/2^{5/2} = Cl_2(4\\alpha) - Cl_2(2\\alpha)$, with $Cl_2(\\theta):=\\sum_{n>0}\\sin(n\\theta)/n^2$ and 1,000-digit precision and readily yields 50,000 digits of $C^{Tet}$, after transformation to an exponentially convergent sum, akin to those studied in math.CA/9803067. It appears that this 3-dimensional result entails a polylogarithmic ladder beginning with the classical formula for $\\pi/\\sqrt2$, in the manner that 4-dimensional results build on that for $\\pi/\\sqrt3$.
Novel phase behaviour of a confined fluid or Ising magnet
Parry, A. O.; Evans, R.
1992-02-01
The phase behaviour of a simple fluid or Ising magnet (at temperatures above its roughening transition) confined between parallel walls that exert opposing surface fields h2 = - h1 is found to be markedly different from that which arises for h2 = h1. Whereas critical wetting plays little role for confinement by identical walls, it is of crucial importance for opposing surface fields. Analysis of a Landau functional and other mean-field treatments show that if h1 is such that critical wetting occurs at a single wall ( L = ∞) at a transition temperature Tw, then phase coexistence, for finite wall separation L, is restricted to temperatures T T > Tw there is a single soft mode phase that is characterized, for zero bulk field and large L, by a +- interface located at the centre of the slit, a transverse correlation length ξ∼≈ eL and a solvation force that is repulsive. For large h1, Tw can lie arbitrarily far below the bulk critical temperature Tc, b. Scaling arguments, whose validity we have confirmed in two dimensions by comparison with exact solutions for interfacial Hamiltonians, predict that such behaviour persists beyond mean-field for systems with short-ranged forces. They also predict similar phase behaviour for long-ranged forces, but with ξ ξ ∼ increasing algebraically with L in the soft mode phase. The solvation force t˜f s changes from repulsive to attractive (at large L) as the temperature is reduced below Tw, i.e. the sign of t˜f s reflects wetting characteristics.
Directory of Open Access Journals (Sweden)
L. Gálisová
2011-03-01
Full Text Available Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.
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.
Excited TBA equations I: Massive tricritical Ising model
Energy Technology Data Exchange (ETDEWEB)
Pearce, Paul A. E-mail: p.pearce@ms.unimelb.edu.au; Chim, Leung E-mail: leung.chim@dsto.defence.gov.au; Ahn, Changrim E-mail: ahn@dante.ewha.ac.kr
2001-05-14
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek{sub 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{sub 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 {chi}{sub 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.
Phase transitions and relaxation dynamics of Ising models exchanging particles
Goh, Segun; Fortin, Jean-Yves; Choi, M. Y.
2017-01-01
A variety of systems in nature and in society are open and subject to exchanging their constituents with other systems (e.g., environments). For instance, in biological systems, cells collect necessary energy and material by exchange of molecules or ions. Similarly, countries, cities or research institutes evolve as their constituents move in or out. To probe the corresponding particle exchange dynamics in such systems, we consider two Ising models exchanging particles and establish a master equation describing the equilibrium phases as well as the non-equilibrium dynamics of the system. It is found that an additional stable phase emerges as a consequence of the particle exchange process. Furthermore, we formulate the Ginzburg-Landau theory which allows to probe correlation effects. Accordingly, critical slowing down is manifested and the associated dynamic exponent is computed in the linear relaxation regime. In particular, this approach is relevant for investigating the grand canonical description of the system plus environment, with particle exchange and state transitions taken into account explicitly.
Allosteric Regulation by a Critical Membrane
Kimchi, Ofer; Machta, Benjamin B
2016-01-01
Many of the processes that underly neural computation are carried out by ion channels embedded in the plasma membrane, a two-dimensional liquid that surrounds all cells. Recent experiments have demonstrated that this membrane is poised close to a liquid-liquid critical point in the Ising universality class. Here we use both exact and stochastic techniques on the lattice Ising model to explore the ramifications of proximity to criticality for proteins that are allosterically coupled to Ising composition modes. Owing to diverging generalized susceptibilities, such a protein's activity becomes strongly influenced by perturbations that influence the two relevant parameters of the critical point, especially the critical temperature. In addition, the protein's kinetics acquire a range of time scales from its surrounding membrane, naturally leading to non-Markovian dynamics.
Interfaces in the confined Ising system with competing surface fields
De Virgiliis, A.; Albano, E. V.; Müller, M.; Binder, K.
2005-07-01
When a magnetic Ising film is confined in a L×M geometry (L≪M) short-range competing magnetic fields ( h1) are applied at opposite walls along the M-direction, a (weakly rounded) localization-delocalization transition of the interface between domains of different orientation that runs parallel to walls can be observed. This transition is the precursor of a wetting phase transition that occurs in the limit of infinite film thickness (L→∞) at the critical curve Tw(h1). For TTw(h1)) such an interface is bound to (unbound from) the walls, while right at Tw(h1) the interface is freely fluctuating around the center of the film. We present extensive Monte Carlo simulations of Ising stripes in the L×M geometry, in order to describe both the localization-delocalization transition and the properties of the delocalized interface. To this aim, we take advantage of several available theoretical results. We make use of a suitable algorithm to define the local position of the interface along the film, such that its probability distribution can be used to account for the transition itself and the fluctuations in the local position of the interface (capillary waves). After describing the interface localization-delocalization transition, we pay attention to the properties of the delocalized interface with an emphasis on the effects of confinement. We analyze several quantities of interest in terms of the film thickness L. The width of the capillary waves (s) can be related to the width of the magnetization profiles (w) by means of a simple approximation. From this relation we estimate a value for the intrinsic width (w0) of the interface which agrees with the theoretical one. Also the correlation length ξ∥ along the film is considered, and the behavior ξ∥∼L2 compares very well to available exact results. Additionally, the interfacial stiffness βΓ obtained from the Fourier spectrum of the capillary waves reproduces the asymptotic theoretical value.
The scaling window of the 5D Ising model with free boundary conditions
Lundow, P. H.; Markström, K.
2016-10-01
The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the conventional scaling picture, where the susceptibility scales as L2 inside a critical scaling window of width 1 /L2. Our results are based on Monte Carlo data gathered on system sizes up to L = 79 (ca. three billion spins) for a wide range of temperatures near the critical point. We analyse the magnetisation distribution, the susceptibility and also the scaling and distribution of the size of the Fortuin-Kasteleyn cluster containing the origin. The probability of this cluster reaching the boundary determines the correlation length, and its behaviour agrees with the mean field critical exponent δ = 3, that the scaling window has width 1 /L2.
2D Ising Model with a Defect Line
Cabra, D C
1994-01-01
We study the two-dimensional Ising model with a defect line and evaluate multipoint energy correlation functions using non-perturbative field-theoretical methods. We also discuss the evaluation of the two spin correlator on the defect line.
Partition function of nearest neighbour Ising models: Some new insights
Indian Academy of Sciences (India)
G Nandhini; M V Sangaranarayanan
2009-09-01
The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.
Application of the Interface Approach in Quantum Ising Models
Sen, Parongama
1997-01-01
We investigate phase transitions in the Ising model and the ANNNI model in transverse field using the interface approach. The exact result of the Ising chain in a transverse field is reproduced. We find that apart from the interfacial energy, there are two other response functions which show simple scaling behaviour. For the ANNNI model in a transverse field, the phase diagram can be fully studied in the region where a ferromagnetic to paramagnetic phase transition occurs. The other region ca...
Monceau, P.; Hsiao, P.-Y.
2003-02-01
We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent yh associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as Df tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when Df is lowered.
Comparison of Ising spin glass noise to flux and inductance noise in SQUIDs.
Chen, Zhi; Yu, Clare C
2010-06-18
Recent experiments implicate spins on the surface of metals as the source of flux and inductance noise in SQUIDs. We present Monte Carlo simulations of 2D and 3D Ising spin glasses that produce magnetization noise S(M) consistent with flux noise. At low frequencies S(M) is a maximum at the critical temperature T(C) in three dimensions, implying that flux noise should be a maximum at T(C). The second spectra of the magnetization noise and the noise in the susceptibility are consistent with experimentally measured SQUID inductance noise.
Minimal duality breaking in the Kallen Lehman approach to 3D Ising model: A numerical test
Astorino, Marco; Canfora, Fabrizio; Martínez, Cristián; Parisi, Luca
2008-06-01
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 model formulation of large scale dynamics universality in the universe
Goldman, T; Laflamme, R
1995-01-01
The partition function of a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field theory, whose critical exponents are calculable and known. This allows one to {\\it compute\\/} the galaxy to galaxy correlation function, whose non--integer exponent is predicted to be between 1.530 and 1.862, to be compared with the phenomenological value of 1.6 to 1.8.
The Peculiar Phase Transitions of the Ising Model on a Small-World Network
Brunson, Trent; Boettcher, Stefan
2009-11-01
To describe many collective phenomena on networks, the Ising model again plays a fundamental role. Here, we study a new network with small-world properties that can be studied exactly with the renormalization group. The network is non-planar and has a recursive design combining a one-dimensional backbone with a hierarchy of long-range bonds. Varying the relative strength between nearest-neighbor and long-range bonds, we can define a one-parameter family of models that exhibits a rich variety of critical phenomena, quite distinct from those on lattice models. Exact results and numerical simulations reveal this behavior in great detail.
Pelizzola, Alessandro
1994-11-01
An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst-van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.
Scaling and universality in the two-dimensional Ising model with a magnetic field.
Mangazeev, Vladimir V; Dudalev, Michael Yu; Bazhanov, Vladimir V; Batchelor, Murray T
2010-06-01
The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.
Quantum correlation and quantum phase transition in the one-dimensional extended Ising model
Zhang, Xi-Zheng; Guo, Jin-Liang
2017-09-01
Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.
Critical Properties of Pure and Random Antiferromagnets
DEFF Research Database (Denmark)
Cowley, R. A.; Carneiro, K.
1980-01-01
Neutron scattering techniques have been used to study the critical properties of CoF2 and the randomly mixed systems: Co/ZnF2 and KMn/NiF3. The results for CoF2 are in excellent accord with the critical properties of the three-dimensional Ising model. In all of the random crystals studied the tra...
Monceau, Pascal; Hsiao, Pai-Yi
2002-09-01
We study the Wolff cluster size distributions obtained from Monte Carlo simulations of the Ising phase transition on Sierpinski fractals with Hausdorff dimensions Df between 2 and 3. These distributions are shown to be invariant when going from an iteration step of the fractal to the next under a scaling of the cluster sizes involving the exponent (β/ν)+(γ/ν). Moreover, the decay of the autocorrelation functions at the critical points enables us to calculate the Wolff dynamical critical exponents z for three different values of Df. The Wolff algorithm is more efficient in reducing the critical slowing down when Df is lowered.
Metastability in an open quantum Ising model
Rose, Dominic C.; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P.
2016-11-01
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.
On Complexity of the Quantum Ising Model
Bravyi, Sergey; Hastings, Matthew
2017-01-01
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local `stoquastic' Hamiltonians with any constant {k ≥ 2}. This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete problem for the complexity class {StoqMA} —an extension of the classical class {MA}. As a corollary, we complete the complexity classification of 2-local Hamiltonians with a fixed set of interactions proposed recently by Cubitt and Montanaro. Secondly, we study quantum annealing algorithms for finding ground states of classical spin Hamiltonians associated with hard optimization problems. We prove that the quantum annealing with TIM Hamiltonians is equivalent modulo polynomial reductions to the quantum annealing with a certain subclass of k-local stoquastic Hamiltonians. This subclass includes all Hamiltonians representable as a sum of a k-local diagonal Hamiltonian and a 2-local stoquastic Hamiltonian.
The Information Service Evaluation (ISE Model
Directory of Open Access Journals (Sweden)
Laura Schumann
2014-06-01
Full Text Available Information services are an inherent part of our everyday life. Especially since ubiquitous cities are being developed all over the world their number is increasing even faster. They aim at facilitating the production of information and the access to the needed information and are supposed to make life easier. Until today many different evaluation models (among others, TAM, TAM 2, TAM 3, UTAUT and MATH have been developed to measure the quality and acceptance of these services. Still, they only consider subareas of the whole concept that represents an information service. As a holistic and comprehensive approach, the ISE Model studies five dimensions that influence adoption, use, impact and diffusion of the information service: information service quality, information user, information acceptance, information environment and time. All these aspects have a great impact on the final grading and of the success (or failure of the service. Our model combines approaches, which study subjective impressions of users (e.g., the perceived service quality, and user-independent, more objective approaches (e.g., the degree of gamification of a system. Furthermore, we adopt results of network economics, especially the "Success breeds success"-principle.
The Gravity Dual of the Ising Model
Castro, Alejandra; Hartman, Thomas; Maloney, Alexander; Volpato, Roberto
2011-01-01
We evaluate the partition function of three dimensional theories of gravity in the quantum regime, where the AdS radius is Planck scale and the central charge is of order one. The contribution from the AdS vacuum sector can - with certain assumptions - be computed and equals the vacuum character of a minimal model CFT. The torus partition function is given by a sum over geometries which is finite and computable. For generic values of Newton's constant G and the AdS radius L the result has no Hilbert space interpretation, but in certain cases it agrees with the partition function of a known CFT. For example, the partition function of pure Einstein gravity with G=3L equals that of the Ising model, providing evidence that these theories are dual. We also present somewhat weaker evidence that the 3-state and tricritical Potts models are dual to pure higher spin theories of gravity based on SL(3) and E_6, respectively.
Directory of Open Access Journals (Sweden)
Rongguo Yan
2016-10-01
Full Text Available There exist several positively and negatively charged electrolytes or ions in human blood, urine, and other body fluids. Tests that measure the concentration of these ions in clinics are performed using a more affordable, portable, and disposable potentiometric sensing method with few sample volumes, which requires the use of ion-selective electrodes (ISEs and reference electrodes. This review summarily descriptively presents progressive developments and applications of ion selective electrodes in medical laboratory electrolytic ion tests, from conventional ISEs, solid-contact ISEs, carbon nanotube based ISEs, to graphene-based ISEs.
Reentrant transitions of a mixed-spin Ising model on the diced lattice
Directory of Open Access Journals (Sweden)
M.Jascur
2005-01-01
Full Text Available Magnetic behaviour of a mixed spin-1/2 and spin-1 Ising model on the diced lattice is studied using an exact star-triangle mapping transformation. It is found that the uniaxial as well as biaxial single-ion anisotropy acting on the spin-1 sites may potentially cause a reentrant transition with two consecutive critical points. Contrary to this, the effect of next-nearest-neighbour interaction between the spin-1/2 sites possibly leads to a reentrant transition with three critical temperatures in addition to the one with two critical points only. The shape of the total magnetization versus temperature dependence is particularly investigated for the case of ferrimagnetically ordered system.
Properties of the interface in the confined Ising magnet with competing surface fields
Albano, Ezequiel V.; de Virgiliis, Andres; Müller, Marcus; Binder, Kurt
2007-02-01
A two-dimensional magnetic Ising system confined in an L×D geometry ( L≪D) in the presence of competing magnetic fields ( h) acting at opposite walls along the D-direction, exhibits an interface between domains of different orientation that run parallel to the walls. In the limit L→∞, this interface undergoes a wetting transition that occurs at the critical curve Tw(h), so that for Tinterface is bound to the walls, while for Tw(h)⩽Tinterface is freely fluctuating around the center of the film, where Tcb is the bulk critical temperature. By considering both short- and long-range magnetic fields acting at the walls, we study the divergence of the (equilibrated) average position of the interface when approaching the wetting critical point. Furthermore, starting from a monodomain structure with the interface bound to one wall, we also study the dynamics of the interface unbinding.
Thermodynamic geometry of a kagome Ising model in a magnetic field
Energy Technology Data Exchange (ETDEWEB)
Mirza, B., E-mail: b.mirza@cc.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Talaei, Z., E-mail: zs_talaie@ph.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of)
2013-02-15
We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive thermodynamic curvature and its components near the criticality. According to standard scaling, scalar curvature R behaves as |β−β{sub c}|{sup α−2} for α>0 where β is the inverse temperature and α is the critical exponent of specific heat. In the model considered here in which α is zero, we found that R behaves as |β−β{sub c}|{sup α−1}.
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.
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.
Mathematical structure of three - dimensional (3D) Ising model
Zhang, Zhi-dong
2013-01-01
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model, Reidemeister moves in the knot theory, Yang-Baxter and tetrahedron equations, the following facts are illustrated for the 3D Ising model: 1) The complexified quaternion basis constructed for the 3D Ising model represents naturally the rotation in a (3 + 1) - dimensional space-time, as a relativistic quantum statistical mechanics model, which is consistent with the 4-fold integrand of the partition function by taking the time average. 2) A unitary transformation with a matrix being a spin representation in 2^(nlo)-space corresponds to a rotation in 2nlo-space, which serves to smooth all the crossings in the transfer matrices and contributes as the non-trivial topologic part of the partition function of the 3D Ising model. 3) A tetrahedron relation would ensure the commutativity o...
Ising systems with pairwise competing surface fields
Energy Technology Data Exchange (ETDEWEB)
Milchev, A [Institut fuer Physik, Johannes Gutenberg-Universitaet, D-55099 Mainz, Staudinger Weg 7 (Germany); Institute for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia (Bulgaria); De Virgiliis, A [Institut fuer Physik, Johannes Gutenberg-Universitaet, D-55099 Mainz, Staudinger Weg 7 (Germany); Binder, K [Institut fuer Physik, Johannes Gutenberg-Universitaet, D-55099 Mainz, Staudinger Weg 7 (Germany)
2005-11-02
The magnetization distribution and phase behaviour of large but finite Ising simple cubic L x L x L lattices in d = 3 dimensions and square L x L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields +H{sub s} act on one pair of opposite boundaries while surface fields -H{sub s} act on the other pair (in d 3, periodic boundary conditions are used for the remaining pair). Both the distribution P{sub L}(m) of the global magnetization and also the distribution of the local magnetization m(x,z) are obtained by Monte Carlo simulations, where x and z denote the coordinates when the boundaries are oriented along the x-axis and z-axis (in d = 2); or along the xy-plane and zy-plane (in d = 3, where the periodic boundary condition applies in the y-direction). Varying the temperature T and linear dimension L it is found that a single bulk rounded phase transition occurs, which converges to the bulk transition temperature T{sub cb} as L {yields} {infinity}, unlike other geometric arrangements of competing boundary fields, where a second transition occurs in the bulk due to interface formation or delocalization, related to wedge or corner filling or wetting transitions, respectively. In the present geometry, only precursors of wetting layers form on those boundaries where the field is oppositely oriented to the magnetization in the bulk and the thickness of these layers is found to scale like L{sup 1/2} (in d = 2) or lnL (in d = 3), respectively. These findings are explained in terms of a phenomenological theory based on the effective interface Hamiltonian and scaling considerations.
Ising systems with pairwise competing surface fields
Milchev, A.; DeVirgiliis, A.; Binder, K.
2005-11-01
The magnetization distribution and phase behaviour of large but finite Ising simple cubic L × L × L lattices in d = 3 dimensions and square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields +Hs act on one pair of opposite boundaries while surface fields -Hs act on the other pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distribution PL(m) of the global magnetization and also the distribution of the local magnetization m(x,z) are obtained by Monte Carlo simulations, where x and z denote the coordinates when the boundaries are oriented along the x-axis and z-axis (in d = 2); or along the xy-plane and zy-plane (in d = 3, where the periodic boundary condition applies in the y-direction). Varying the temperature T and linear dimension L it is found that a single bulk rounded phase transition occurs, which converges to the bulk transition temperature Tcb as L \\rightarrow \\infty , unlike other geometric arrangements of competing boundary fields, where a second transition occurs in the bulk due to interface formation or delocalization, related to wedge or corner filling or wetting transitions, respectively. In the present geometry, only precursors of wetting layers form on those boundaries where the field is oppositely oriented to the magnetization in the bulk and the thickness of these layers is found to scale like L1/2 (in d = 2) or lnL (in d = 3), respectively. These findings are explained in terms of a phenomenological theory based on the effective interface Hamiltonian and scaling considerations.
Critical phenomena in the majority voter model on two-dimensional regular lattices.
Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl
2014-05-01
In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.
Cosmic ray composition investigations using ICE/ISEE-3
Wiedenbeck, Mark E.
1992-01-01
The analysis of data from the high energy cosmic experiment on ISEE-3 and associated modeling and interpretation activities are discussed. The ISEE-3 payload included two instruments capable of measuring the composition of heavy cosmic rays. The designs of these two instruments incorporated innovations which made it possible, for the first time, to measure isotopic as well as the chemical composition for a wide range of elements. As the result of the demonstrations by these two instruments of the capability to resolve individual cosmic ray isotopes, a new generation of detectors was developed using very similar designs, but having improved reliability and increased sensitive area. The composition measurements which were obtained from the ISEE-3 experiment are summarized.
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.
Random field Ising model and community structure in complex networks
Son, S.-W.; Jeong, H.; Noh, J. D.
2006-04-01
We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field Bs = +∞, Bt = -∞, and Bi≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)
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.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
赛灵思公司（Xilinx）日前宣布推出集成软件环境（ISE）设计工其套件8．1i版，新版本增加了新的ISE Fmax技术，具有增强的物理综合能力，可提高Virtex-4和Spartan-3架构的性能和时序收敛特性。ISF8．1i还对局部重配置技术进行了增强，可实现更低的成本、更小、的尺寸和更低的功耗。
Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model
Institute of Scientific and Technical Information of China (English)
Guo Yun-Jun; Wang Ke-Feng; Liu Jun-Ming
2009-01-01
An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca3CoMnO6, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca3Co2-xMnxO6 (x≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.
Testing Efficiency of Derivative Markets: ISE30, ISE100, USD and EURO
Directory of Open Access Journals (Sweden)
Mustafa Akal,
Full Text Available This study attempts to develop new market efficiency tests depending on the spot and future prices, or the differences of them alternative to traditional unit root test build on univariate time series. As a result of the autocorrelation, normality and run tests applied to spot and futures prices or differences of them, and Adopted Purchasing Power Parity test based on a regression the future markets of ISE30, ISE100 index indicators, USD and Euro currencies, all of which have been traded dailly in the Izmir Futures and Options Market for five years, are found inefficient. Autocorrelation, normality and run tests on the differences between spot and futures prices series, and Adopted Purchasing Power Parity test, or autocorrelation, normality and run tests test based on spot series all rejected “the acceptance of efficient market hypothesis” under the existence of unit root in a series. The results of autocrrelation, normality and run tests based on univariate series are found contradictory to the unit root test result. As a result, the acceptance of “efficient market hypothesis” under the existence of unit root is not supported by alternative tests developed in this study. It is suggested that efficiency test shall be stepping on the spot and futures prices; differences of them or Adopted Purchasing Power Parity test developed here rather than unit root test based on univariate series, which is also not appropriate to the definition of futures market efficiency. In addition, one must be sure that the errors disturbances are randomized in deciding whether market is efficient or not.
Ising Model Coupled to Three-Dimensional Quantum Gravity
Baillie, C F
1992-01-01
We have performed Monte Carlo simulations of the Ising model coupled to three-dimensional quantum gravity based on a summation over dynamical triangulations. These were done both in the microcanonical ensemble, with the number of points in the triangulation and the number of Ising spins fixed, and in the grand canoncal ensemble. We have investigated the two possible cases of the spins living on the vertices of the triangulation (``diect'' case) and the spins living in the middle of the tetrahedra (``dual'' case). We observed phase transitions which are probably second order, and found that the dual implementation more effectively couples the spins to the quantum gravity.
Bipartition Polynomials, the Ising Model, and Domination in Graphs
Directory of Open Access Journals (Sweden)
Dod Markus
2015-05-01
Full Text Available This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph invariants. We apply this approach to show that, analogously to the Tutte polynomial, the Ising polynomial introduced by Andrén and Markström in [3], can be represented as a sum over spanning forests.
Entanglement and quantum phase transition in the Heisenberg-Ising model
Institute of Scientific and Technical Information of China (English)
Tan Xiao-Dong; Jin Bai-Qi; Gao Wei
2013-01-01
We use the quantum renormalization-group (QRG) method to study the entanglement and quantum phase transition (QPT) in the one-dimensional spin-l/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.(N.Y.)16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.
Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles with core-shell structure
Deviren, Bayram; Şener, Yunus
2015-07-01
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.
Hierarchy of correlations for the Ising model in the Majorana representation
Gómez-León, Álvaro
2017-08-01
We study the quantum Ising model in D dimensions with the equation-of-motion technique and the Majorana representation for spins. The decoupling scheme used for the Green's functions is based on the hierarchy of correlations in position space. To lowest order, this method reproduces the well-known mean field phase diagram and critical exponents. When correlations between spins are included, we show how the appearance of thermal fluctuations and magnons strongly affects the physical properties. In one dimension and for B =0 we demonstrate that, to first order in correlations, thermal fluctuations completely destroy the ordered phase. For nonvanishing transverse field we show that the model exhibits different behavior than its classical counterpart, especially near the quantum critical point. We discuss the connection with the Dyson's equation formalism and the explicit form of the self-energies.
Scaling of geometric phase versus band structure in cluster-Ising models
Nie, Wei; Mei, Feng; Amico, Luigi; Kwek, Leong Chuan
2017-08-01
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z =1 or z =2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.
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.
Nonequilibrium dynamical phase transition of 3D kinetic Ising/Heisenberg spin system
Institute of Scientific and Technical Information of China (English)
Shao Yuan-Zhi; Lai J. K. L.; Shek C. H.; Lin Guang-Ming; Lan Tu
2004-01-01
We have studied the nonequilibrium dynamic phase transitions of both three-dimensional (3D) kinetic Ising and Heisenberg spin systems in the presence of a perturbative magnetic field by Monte Carlo simulation. The feature of the phase transition is characterized by studying the distribution of the dynamical order parameter.In the case of anisotropic Ising spin system (ISS), the dynamic transition is discontinuous and continuous under low and high temperatures respectively, which indicates the existence of a tri-critical point (TCP) on the phase boundary separating low-temperature order phase and high-temperature disorder phase. The TCP shifts towards the higher temperature region with the decrease of frequency, I.e. TTCp=1.33×exp(-ω/30.7). In the case of the isotropic Heisenberg spin system (HSS), however, the situation on dynamic phase transition of HSS is quite different from that of ISS in that no stable dynamical phase transition was observed in kinetic HSS after a threshold time. The evolution of magnetization in the HSS driven by a symmetrical external field after a certain duration always tends asymptotically to a disorder state no matter what an initial state the system starts with. The threshold time τ depends upon the amplitude H0,reduced temperature T/TC and the frequency ωas τ=C·ωα·H-β0·(T/TC)-γ.
A Monte Carlo study of thin spin-1 Ising films with surface exchange enhancement
Tucker, J W
2000-01-01
Using extensive Monte Carlo simulations the effect of surface exchange enhancement on ultrathin spin-1 Ising films (having simple cubic symmetry) ranging in thickness from L=3 to 8 atomic layers, has been studied. The simulations were performed on systems containing up to just over 15000 spins with periodic boundary conditions imposed in directions perpendicular to the film thickness. Within the resolution of the Monte Carlo data, it was concluded that the ratio of surface to bulk exchange interaction strengths, J sub s /J sub b) sub c sub r sub i sub t , at which the critical temperatures of the film and bulk material were equal, was independent of L, as predicted by mean field and effective field theories. However, the value of J sub s /J sub b) sub c sub r sub i sub t is spin dependent. It was found that for the spin-1 Ising films, J sub s /J sub b) sub c sub r sub i sub t =1.45, significantly below the value 1.52 obtained by Monte Carlo simulation for the spin ((1)/(2)) system reported in the literature.
Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model
Jalabert, Rodolfo A.; Sachdev, Subir
1991-07-01
The Ising model on a three-dimensional cubic lattice with all plaquettes in the x-y frustrated plane is studied by use of a Monte Carlo technique; the exchange constants are of equal magnitude, but have varying signs. At zero temperature, the model has a finite entropy and no long-range order. The low-temperature phase is characterized by an order parameter measuring the openZ4 symmetry of lattice rotations which is invariant under Mattis gauge transformation; fluctuations lead to the alignment of frustrated bonds into columns and a fourfold degeneracy. An additional factor-of-2 degeneracy is obtained from a global spin flip. The order vanishes at a critical temperature by a transition that appears to be in the universality class of the D=3, XY model. These results are consistent with the theoretical predictions of Blankschtein et al. This Ising model is related by duality to phenomenological models of two-dimensional frustrated quantum antiferromagnets.
Vink, R L C; Fischer, T; Binder, K
2010-11-01
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.
The Relationship between Macroeconomic Variables and ISE Industry Index
Directory of Open Access Journals (Sweden)
Ahmet Ozcan
2012-01-01
Full Text Available In this study, the relationship between macroeconomic variables and Istanbul Stock Exchange (ISE industry index is examined. Over the past years, numerous studies have analyzed these relationships and the different results obtained from these studies have motivated further research. The relationship between stock exchange index and macroeconomic variables has been well documented for the developed markets. However, there are few studies regarding the relationship between macroeconomic variables and stock exchange index for the developing markets. Thus, this paper seeks to address the question of whether macroeconomic variables have a significant relationship with ISE industry index using monthly data for the period from 2003 to 2010. The selected macroeconomic variables for the study include interest rates, consumer price index, money supply, exchange rate, gold prices, oil prices, current account deficit and export volume. The Johansen’s cointegration test is utilized to determine the impact of selected macroeconomic variables on ISE industry index. The result of the Johansen’s cointegration shows that macroeconomic variables exhibit a long run equilibrium relationship with the ISE industry index.
A new efficient Cluster Algorithm for the Ising Model
Nyffeler, M; Wiese, U J; Nyfeler, Matthias; Pepe, Michele; Wiese, Uwe-Jens
2005-01-01
Using D-theory we construct a new efficient cluster algorithm for the Ising model. The construction is very different from the standard Swendsen-Wang algorithm and related to worm algorithms. With the new algorithm we have measured the correlation function with high precision over a surprisingly large number of orders of magnitude.
Non-conventional Superconductors and diluted Ising Model
Ni, Xuan Zhong
2016-01-01
This paper demonstrates that the results of a Monte Carlo simulation of a diluted 2D Ising antiferromagnetic system corresponds with the phase diagram for non conventional superconductors. An energy gap of this system is defined. We also find a strange phenomenon that when the lattice size of simulation increased the crystal structure becomes more like quasi crystal at the low temperature.
Topological Structures of Cluster Spins for Ising Models
Feng, You-gang
2010-01-01
We discussed hierarchies and rescaling rule of the self similar transformations in Ising models, and define a fractal dimension of an ordered cluster, which minimum corresponds to a fixed point of the transformations. By the fractal structures we divide the clusters into two types: irreducible and reducible. A relationship of cluster spin with its coordination number and fractal dimension is obtained.
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
Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway.
Millership, C; Phillips, J J; Main, E R G
2016-05-08
Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.
Ising model on the generalized Bruhat-Tits tree
Zinoviev, Yu. M.
1991-08-01
The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.
Internet Access to ISEE-1 and 2 Magnetometer Data
1997-01-01
It is reported that the entire ISEE-1 and -2 magnetometer data are placed on-line, using an 8 Gbyte disk drive. The data are stored at 4-s and 60-s resolution. Also, an interactive world wide web page, which allows to plot, on request, any interval for which magnetometer data are available, is developed.
Proceedings of the ISES Millennium Solar Forum 2000. 1. ed.
Energy Technology Data Exchange (ETDEWEB)
Estrada, Claudio A. [ed.
2000-07-01
The ISES Millennium Solar Forum 2000 was organized by the Association Nacional de Energia Solar (ANES) of Mexico, and the International Solar Energy Society (ISES), in collaboration with other national and international organizations from 17 to 22 of September, 2000 in Mexico City. The Scientific-Technical Conference forms the core of this forum. This comprises of 167 papers, which were presented orally and form part of the proceedings. The papers represent the results of research and technological development effort in Renewable Energy reported by professionals and students of 22 countries. Of course, a major component is from Mexico and Latin America. Here you will find useful information on the advances in different fields of Renewable Energy. [Spanish] La Asociacion Nacional de Energia Solar A.C. (ANES) y la International Solar Society (ISES), apoyadas por organizaciones nacionales e internacionales, comprometidas con la promocion de las energias renovables organizaron el ISES Millennium Solar Forum 2000, los dias 17 a 22 de septiembre del 2000 en la Ciudad de Mexico. Como parte medular de este foro se organizo la reunion cientifico-tecnica, en donde se presentaron 167 trabajos, la mayoria de los cuales se incluyen en esta memoria. Estos trabajos representan el esfuerzo en investigacion y desarrollo tecnologico de estudiantes y profesionales de mas de 22 paises, la mayoria de Mexico y America Latina. En esta memoria se encuentran los avances mas relevantes en las distintas areas de especializacion de las energias renovables.
Phase transitions for continuous-spin Ising ferromagnets
Beijeren, H. van; Sylvester, G.S.
1978-01-01
We study the comparison of continuous-spin ferromagnetic Ising models which differ only in their a priori single-spin weighting measures, and characterize the relationship of two even weighting measures ν′, ν on R such that the spin expectations of any ferromagnet with single-spin weighting measure
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.
Shimada, Hirohiko; Hikami, Shinobu
2016-12-01
The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the O( N) models from N=1 (Ising model) to N=0 (polymer). Even for non-integer N, the O( N) sum rule allows one to study the unitarity bound formally defined from the positivity, which may be violated in a non-unitary CFT. This unitarity bound of the scaling dimension for the O( N)-symmetric-tensor develops a kink as a function of the fundamental field as in the case of the energy operator dimension in the Z_2 (Ising) sum rule. Although this kink structure becomes less pronounced as N tends to zero, we found instead an emerging asymmetric minimum in the current central charge C_J. Despite the non-unitarity of the O( N) model at non-integer N, we find the C_J-kink along the unitarity bound lies very close to the location of the infrared (IR) O( N) CFT estimated by other methods. It is pointed out that certain level degeneracies at the IR CFT should induce these singular shapes of the unitarity bounds. As an application to the quantum and classical spin systems, we also predict critical exponents associated with the N=1 supersymmetry, which could be relevant for locating the corresponding fixed point in the phase diagram.
Thermal entanglement of the Ising Heisenberg diamond chain with Dzyaloshinskii Moriya interaction
Institute of Scientific and Technical Information of China (English)
谯洁; 周斌
2015-01-01
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisen-berg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction con-tributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interac-tion, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters (Dz and Dx) have remarkably different infl uences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx , and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz.
Corner wetting in the two-dimensional Ising model: Monte Carlo results
Albano, E. V.; DeVirgiliis, A.; Müller, M.; Binder, K.
2003-01-01
Square L × L (L = 24-128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T interface is localized either close to the lower left corner or close to the upper right corner. Numerous theoretical predictions for the critical behaviour of this 'corner wetting' or 'wedge filling' transition are tested by Monte Carlo simulations. In particular, it is shown that for T = Tf (h) the magnetization profile m(z) in the z-direction normal to the interface is simply linear and the interfacial width scales as w propto L, while for T > Tf (h) it scales as w proptosurd L. The distribution P (ell) of the interface position ell (measured along the z-direction from the corners) decays exponentially for T Tf (h). Furthermore, the Monte Carlo data are compatible with langleellrangle propto (Tf (h) - T)-1 and a finite size scaling of the total magnetization according to M(L, T) = tilde M {(1 - T/Tf (h))nubot L} with nubot = 1. Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.
Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu
2016-08-01
In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.
Directory of Open Access Journals (Sweden)
Nicolás A De La Espriella
2012-01-01
Full Text Available Mediante simulaciones de Monte Carlo, se analizan las propiedades magnéticas de un modelo ferrimagnético de Ising mixto, con espines S = ±3/2, ±1/2 y σ = ±5/2, ±3/2, ±1/2 distribuidos sobre una red cuadrada, con diferentes anisotropías. Se supuso que la interacción de intercambio a primeros vecinos, J1, entre espines S y σ es antiferromagnética (J1 Using Monte Carlo simulations, the magnetic properties of a mixed Ising ferrimagnetic model with spins S = ±3/2, ±1/2 y σ = ±5/2, ±3/2, ±1/2 distributed on a square lattice with different anisotropies was analyzed. It was assumed that the exchange interaction to nearest neighbors, J1, between spins S and σ, is antiferromagnetic (J1 < 0. Also, it was considered that the effect of the intensities of the single-ion anisotropies, due to the crystalline fields of the sublattices S and σ, Ds and Dj respectively. The existence and dependence of the compensation temperature in the model with respect to the single-ion anisotropies was also studied. By fixing the parameter Ds and varying the intensity of Dj it probable phase transitions of first order appear. The analysis of the critical temperatures is obtained through the maximum of the specific heat of the system. Phase diagrams at finite temperatures are obtained in the temperature-anisotropy plane.
Spin-3/2 Ising model AFM/AFM two-layer lattice with crystal field
Institute of Scientific and Technical Information of China (English)
Erhan Albayrak; Ali Yigit
2009-01-01
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 the 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 is also found that the system exhibits double-critical end points and isolated points. The model aiso presents two Néel temperatures, T_N, and the existence of which leads to the reentrant behaviour.
Mixed spin Ising model with four-spin interaction and random crystal field
Energy Technology Data Exchange (ETDEWEB)
Benayad, N., E-mail: n.benayad@fsac.ac.ma [Groupe de Mecanique Statistique, Laboratoire de physique theorique et appliquee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Laboratoire de physique des hautes energies et de la matiere condensee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Ghliyem, M. [Groupe de Mecanique Statistique, Laboratoire de physique theorique et appliquee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco); Laboratoire de physique des hautes energies et de la matiere condensee, Faculte des sciences-Aien Chock, Universite Hassan II-Casablanca, B.P 5366 Maarif, Casablanca 20100 (Morocco)
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.
Magnetic Quantum Phase Transitions of a Kondo Lattice Model with Ising Anisotropy
Zhu, Jian-Xin; Kirchner, Stefan; Si, Qimiao; Grempel, Daniel R.; Bulla, Ralf
2006-03-01
We study the Kondo Lattice model with Ising anisotropy, within an extended dynamical mean field theory (EDMFT) in the presence or absence of antiferromagnetic ordering. The EDMFT equations are studied using both the Quantum Monte Carlo (QMC) and Numerical Renormalization Group (NRG) methods. We discuss the overall magnetic phase diagram by studying the evolution, as a function of the ratio of the RKKY interaction and bare Kondo scale, of the local spin susceptibility, magnetic order parameter, and the effective Curie constant of a nominally paramagnetic solution with a finite moment. We show that, within the numerical accuracy, the quantum magnetic transition is second order. The local quantum critical aspect of the transition is also discussed.
The square lattice Ising model on the rectangle I: Finite systems
Hucht, Alfred
2016-01-01
The partition function of the square lattice Ising model on the rectangle is calculated exactly for arbitrary system size $L\\times M$ and temperature. We start with the dimer method of Kasteleyn, McCoy & Wu, construct a highly symmetric block transfer matrix and derive a factorization of the involved determinant, effectively decomposing the free energy into two parts, $F(L,M)=F_{\\infty}^{\\leftrightarrow}(L,M)+F_\\mathrm{res}^{\\leftrightarrow}(L,M)$. The residual part $F_\\mathrm{res}^{\\leftrightarrow}(L,M)$ contains the nontrivial finite-size contributions and becomes exponentially small for large $L/M$ and off-critical temperatures. It is given by the determinant of a $\\frac{M}{2}\\times\\frac{M}{2}$ matrix and can be mapped onto an effective spin model with $M$ spins and long-range interactions. The relations to the Casimir potential and the Casimir force scaling functions are discussed.
High-Temperature Cutoff Approximation of the 3D Kinetic Ising Model
Institute of Scientific and Technical Information of China (English)
ZHU JianYang; YANG ZhanRu
2001-01-01
A single-spin transition critical dynamics is used to investigate the three-dimensional kinetic Ising model on an anisotropic cubic lattice. We first derive the fundamental dynamical equations, and then linearize them by a cutoff approximation. We obtain the approximate solutions of the local magnetization and equal-time pair correlation function in zero field. In which the axial-decoupling terms γ1γ2, γ2γ3 and γ1γ3 as higher infinitesimal quantity are ignored, where γa = tanh(2kα) = tanh(2Jα/kβT) (α = 1,2,3). We think that it is reasonable as the temperature of the system is very high. The result of what we obtain in this paper can go back to the one-dimensional Glauber's theory as long as k2 = k3= 0.
The cellular Ising model: a framework for phase transitions in multicellular environments.
Weber, Marc; Buceta, Javier
2016-06-01
Inspired by the Ising model, we introduce a gene regulatory network that induces a phase transition that coordinates robustly the behaviour of cell ensembles. The building blocks of the design are the so-called toggle switch interfaced with two quorum sensing modules, Las and Lux. We show that as a function of the transport rate of signalling molecules across the cell membrane the population undergoes a spontaneous symmetry breaking from cells individually switching their phenotypes to a global collective phenotypic organization. By characterizing the critical behaviour, we reveal some properties, such as phenotypic memory and hypersensitivity, with relevance in the field of synthetic biology. We argue that our results can be extrapolated to other multicellular systems and be a generic framework for collective decision-making processes. © 2016 The Author(s).
Depinning transition and thermal fluctuations in the random-field Ising model.
Roters, L; Hucht, A; Lübeck, S; Nowak, U; Usadel, K D
1999-11-01
We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.
Properties of Interfaces in the two and three dimensional Ising Model
Berg, B A; Neuhaus, T; 10.1007/BF02198159
2009-01-01
To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^\\mu$ to be $F^s_0 = 1.52 \\pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.
Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models
Giuliani, Alessandro; Mastropietro, Vieri
2013-11-01
We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.
Monte Carlo simulations of an Ising bilayer with non-equivalent planes
Diaz, I. J. L.; Branco, N. S.
2017-02-01
We study the thermodynamic and magnetic properties of an Ising bilayer ferrimagnet. The system is composed of two interacting non-equivalent planes in which the intralayer couplings are ferromagnetic while the interlayer interactions are antiferromagnetic. Moreover, one of the planes is randomly diluted. The study is carried out within a Monte Carlo approach employing the multiple histogram reweighting method and finite-size scaling tools. The occurrence of a compensation phenomenon is verified and the compensation temperature, as well as the critical temperature for the model, are obtained as functions of the Hamiltonian parameters. We present a detailed discussion of the regions of the parameter space where the compensation effect is present or absent. Our results are then compared to a mean-field-like approximation applied to the same model by Balcerzak and Szałowski (2014). Although the Monte Carlo and mean-field results agree qualitatively, our quantitative results are significantly different.
OPE Coefficients of the 3D Ising model with a trapping potential
Costagliola, Gianluca
2015-01-01
Recently the OPE coefficients of the 3D Ising model universality class have been calculated by studying the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a non uniform potential acting as a trap. This setting is described by the trap size scaling ansatz, that can be combined with the general framework of the conformal perturbation in order to write down the correlators $$, $$ and $$, from which the OPE coefficients can be estimated. We find $C^{\\sigma}_{\\sigma\\epsilon}= 1.051(3)$ , in agreement with the results already known in the literature, and $C^{\\epsilon}_{\\epsilon\\epsilon}= 1.32 (15)$ , confirming and improving the previous estimate obtained in the uniform perturbation case.
Applicability of n-vicinity method for calculation of free energy of Ising model
Kryzhanovsky, Boris; Litinskii, Leonid
2017-02-01
Here we apply the n-vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D-dimensional hypercube lattice. We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy. As expected, for large dimensions (D ≥ 3) the system demonstrates a phase transition of the second kind. In this case, we obtain a simple analytical expression for the critical value of the inverse temperature. When 3 ≤ D ≤ 7 this expression is in a very good agreement with the results of computer simulations. In the case of small dimensions (D = 1 , 2), there is a noticeable discrepancy with the known exact results.
Thermodynamical Properties of Spin-3／2 Ising Model in a Longitudinal Random Field with Crystal Field
Institute of Scientific and Technical Information of China (English)
LIANGYa-Qiu; WEIGuo-Zhu; ZHANGHong; SONGGuo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.
Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field
Institute of Scientific and Technical Information of China (English)
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Hong; SONG Guo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.
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.
The 2014 Earth return of the ISEE-3/ICE spacecraft
Dunham, David W.; Farquhar, Robert W.; Loucks, Michel; Roberts, Craig E.; Wingo, Dennis; Cowing, Keith L.; Garcia, Leonard N.; Craychee, Tim; Nickel, Craig; Ford, Anthony; Colleluori, Marco; Folta, David C.; Giorgini, Jon D.; Nace, Edward; Spohr, John E.; Dove, William; Mogk, Nathan; Furfaro, Roberto; Martin, Warren L.
2015-05-01
In 1978, the 3rd International Sun-Earth Explorer (ISEE-3) became the first libration-point mission, about the Sun-Earth L1 point. Four years later, a complex series of lunar swingbys and small propulsive maneuvers ejected ISEE-3 from the Earth-Moon system, to fly by a comet (Giacobini-Zinner) for the first time in 1985, as the rechristened International Cometary Explorer (ICE). In its heliocentric orbit, ISEE-3/ICE slowly drifted around the Sun to return to the Earth's vicinity in 2014. Maneuvers in 1986 targeted a 2014 August 10th lunar swingby to recapture ISEE-3 into Earth orbit. In 1999, ISEE-3/ICE passed behind the Sun; after that, tracking of the spacecraft ceased and its control center at Goddard was shut down. In 2013, meetings were held to assess the viability of "re-awakening" ISEE-3. The goal was to target the 2014 lunar swingby, to recapture the spacecraft back into a halo-like Sun-Earth L1 orbit. However, special hardware for communicating with the spacecraft via NASA's Deep Space Network stations was discarded after 1999, and NASA had no funds to reconstruct the lost equipment. After ISEE-3's carrier signal was detected on March 1st with the 20 m antenna at Bochum, Germany, Skycorp, Inc. decided to initiate the ISEE-3 Reboot Project, to use software-defined radio with a less costly S-band transmitter that was purchased with a successful RocketHub crowdsourcing effort. NASA granted Skycorp permission to command the spacecraft. Commanding was successfully accomplished using the 300 m radio telescope at Arecibo. New capture trajectories were computed, including trajectories that would target the August lunar swingby and use a second ΔV (velocity change) that could target later lunar swingbys that would allow capture into almost any desired final orbit, including orbits about either the Sun-Earth L1 or L2 points, a lunar distant retrograde orbit, or targeting a flyby of the Earth-approaching active Comet Wirtanen in 2018. A tiny spinup maneuver was
Exploring ISEE-3 magnetic cloud polarities with electron heat fluxes
Energy Technology Data Exchange (ETDEWEB)
Kahler, S.W. [Air Force Research Laboratory, 29 Randolph Rd, Hanscom AFB, Massachusetts 01731 (United States); Crooker, N.U. [Center for Space Physics, Boston University, 725 Commonwealth Ave., Boston, Massachusetts 02215 (United States); Gosling, J.T. [Los Alamos National Laboratory, MS D 466, Los Alamos, New Mexico 87545 (United States)
1999-06-01
We have used solar wind electron heat fluxes to determine the magnetic polarities of the interplanetary magnetic fields (IMF) during the ISEE-3 observations in 1978{endash}1982. That period included 14 magnetic clouds (MCs) identified by Zhang and Burlaga. The MCs have been modeled as single magnetic flux ropes, and it is generally assumed that they are magnetically closed structures with each end of the flux rope connected to the Sun. The flux rope model is valid only if the magnetic polarity of each MC does not change during the passage of ISEE-3 through the MC. We test this model with the heat flux data, using the dominant heat flux in bidirectional electron heat fluxes to determine the MC polarities. The polarity changes within at least 2, and possibly 6, of the 14 MCs, meaning that those MCs can not fit the model of a single flux rope. {copyright} {ital 1999 American Institute of Physics.}
Exploring ISEE-3 magnetic cloud polarities with electron heat fluxes
Kahler, S. W.; Crooker, N. U.; Gosling, J. T.
1999-06-01
We have used solar wind electron heat fluxes to determine the magnetic polarities of the interplanetary magnetic fields (IMF) during the ISEE-3 observations in 1978-1982. That period included 14 magnetic clouds (MCs) identified by Zhang and Burlaga. The MCs have been modeled as single magnetic flux ropes, and it is generally assumed that they are magnetically closed structures with each end of the flux rope connected to the Sun. The flux rope model is valid only if the magnetic polarity of each MC does not change during the passage of ISEE-3 through the MC. We test this model with the heat flux data, using the dominant heat flux in bidirectional electron heat fluxes to determine the MC polarities. The polarity changes within at least 2, and possibly 6, of the 14 MCs, meaning that those MCs can not fit the model of a single flux rope.
Ising Spectroscopy II: Particles and poles at T>Tc
Zamolodchikov, Alexander
2013-01-01
I discuss particle content of the Ising field theory (the scaling limit of the Ising model in a magnetic field), in particular the evolution of its mass spectrum under the change of the scaling parameter. I consider both real and pure imaginary magnetic field. Here I address the high-temperature regime, where the spectrum of stable particles is relatively simple (there are from one to three particles, depending on the parameter). My goal is to understand analytic continuations of the masses to the domain of the parameter where they no longer exist as the stable particles. I use the natural tool -- the $2\\to 2$ elastic scattering amplitude, with its poles associated with the stable particles, virtual and resonance states in a standard manner. Concentrating attention on the "real" poles (those corresponding to stable and virtual states) I propose a scenario on how the pattern of the poles evolves from the integrable point $T=T_c,\\ H\
OpenCL Implementation of NeuroIsing
Zapart, C. A.
Recent advances in graphics card hardware combined with anintroduction of the OpenCL standard promise to accelerate numerical simulations across diverse scientific disciplines. One such field benefiting from new hardware/software paradigms is econophysics. The paper describes an OpenCL implementation of a selected econophysics model: NeuroIsing, which has been designed to execute in parallel on a vendor-independent graphics card. Originally introduced in the paper [C.~A.~Zapart, ``Econophysics in Financial Time Series Prediction'', PhD thesis, Graduate University for Advanced Studies, Japan (2009)], at first it was implemented on a CELL processor running inside a SONY PS3 games console. The NeuroIsing framework can be applied to predicting and trading foreign exchange as well as stock market index futures.
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.
Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
Brell, Courtney G.; Burton, Simon; Dauphinais, Guillaume; Flammia, Steven T.; Poulin, David
2014-07-01
We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range from 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.
Limiting shapes in two-dimensional Ising ferromagnets.
Krapivsky, P L; Olejarz, Jason
2013-06-01
We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.
Ising Spin-Based Error Correcting Private-Key Cryptosystems
Institute of Scientific and Technical Information of China (English)
ZHENG Dong; ZHENG Yan-fei; FAN Wu-ying
2006-01-01
Ising spin system has been shown to provide a new class of error-correction code and can be used to construct public-key cryptosystems by making use of statistical mechanics. The relation between Ising spin systems and private-key cryptosystems are investigated. Two private-key systems are based on two predetermined randomly constructed sparse matrices and rely on exploiting physical properties of the Mackay-Neal (MN) low-density parity-check (LDPC) error-correcting codes are proposed. One is error correcting private-key system, which is powerful to combat ciphertext errors in communications and computer systems. The other is a private-key system with authentication.
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.
Ecological risk assessment of TBT in Ise Bay.
Yamamoto, Joji; Yonezawa, Yoshitaka; Nakata, Kisaburo; Horiguchi, Fumio
2009-02-01
An ecological risk assessment of tributyltin (TBT) in Ise Bay was conducted using the margin of exposure (MOE) method. The assessment endpoint was defined to protect the survival, growth and reproduction of marine organisms. Sources of TBT in this study were assumed to be commercial vessels in harbors and navigation routes. Concentrations of TBT in Ise Bay were estimated using a three-dimensional hydrodynamic model, an ecosystem model and a chemical fate model. Estimated MOEs for marine organisms for 1990 and 2008 were approximately 0.1-2.0 and over 100 respectively, indicating a declining temporal trend in the probability of adverse effects. The chemical fate model predicts a much longer persistence of TBT in sediments than in the water column. Therefore, it is necessary to monitor the harmful effects of TBT on benthic organisms.
Ising Processing Units: Potential and Challenges for Discrete Optimization
Energy Technology Data Exchange (ETDEWEB)
Coffrin, Carleton James [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Nagarajan, Harsha [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bent, Russell Whitford [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-07-05
The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and bench- marking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one example of a commercially available Ising processing unit.
Microcanonical Phase Diagram of the BEG and Ising Models
Institute of Scientific and Technical Information of China (English)
李粮生; 郑宁; 史庆藩
2012-01-01
The density of states of long-range Blume-Emery-Criffiths （BEG） and short-range lsing models are obtained by using Wang-Landau sampling with adaptive windows in energy and magnetization space. With accurate density of states, we are able to calculate the mierocanonical specific heat of fixed magnetization introduced by Kastner et al. in the regions of positive and negative temperature. The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane. However the phase diagram of the long-range model constructed by peaks of the microeanonieal specific heat looks obviously different from the Ising chart.
Review of the ISEE-3 geotail magnetic field results
Energy Technology Data Exchange (ETDEWEB)
Tsurutani, B.T.; Goldstein, B.E.; Burton, M.E.; Jones, D.E.
1986-10-01
This review presents a summary of past work on the ISEE-3 distant tail magnetic field observations. An attempt has been made to bring the many results together as a coherent whole, in the hope that the reader can envision the direction of future research necessary to achieve an understanding of the dynamics of the magnetotail from 60 to 240 Rsub(e) and perhaps beyond.
Magnetic properties of mixed Ising system with random field
Institute of Scientific and Technical Information of China (English)
Liang Ya-Qiu; Wei Guo-Zhu; Zhang Qi; Qiu Wei; Zang Shu-Liang
2004-01-01
A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.
A review of the ISEE-3 geotail magnetic field results
Tsurutani, B. T.; Goldstein, B. E.; Burton, M. E.; Jones, D. E.
1986-01-01
This review presents a summary of past work on the ISEE-3 distant tail magnetic field observations. An attempt has been made to bring the many results together as a coherent whole, in the hope that the reader can envision the direction of future research necessary to achieve an understanding of the dynamics of the magnetotail from 60 to 240 earth radii and perhaps beyond.
Minor magnetization loops in two-dimensional dipolar Ising model
Energy Technology Data Exchange (ETDEWEB)
Sarjala, M. [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland); Seppaelae, E.T., E-mail: eira.seppala@nokia.co [Nokia Research Center, Itaemerenkatu 11-13, FI-00180 Helsinki (Finland); Alava, M.J., E-mail: mikko.alava@tkk.f [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland)
2011-05-15
The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M{approx}exp(-{alpha}N{sub l}) where N{sub l} is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.
Exact interface model for wetting in the planar Ising model
Upton, P. J.
1999-10-01
At the wetting transition in the two-dimensional Ising model the long contour (interface) gets depinned from the substrate. It is found that on sufficiently large length scales the statistics of the long contour are described by a unique probability measure corresponding to a continuous ``interface model'' with an interface binding ``potential'' given by a Dirac δ function supported on the substrate. A lattice solid-on-solid model is shown to give similar results.
Complete wetting in the three-dimensional transverse Ising model
Harris, A B; Micheletti, C.; Yeomans, J. M.
1996-01-01
We consider a three-dimensional Ising model in a transverse magnetic field, $h$ and a bulk field $H$. An interface is introduced by an appropriate choice of boundary conditions. At the point $(H=0,h=0)$ spin configurations corresponding to different positions of the interface are degenerate. By studying the phase diagram near this multiphase point using quantum-mechanical perturbation theory we show that that quantum fluctuations, controlled by $h$, split the multiphase degeneracy giving rise...
Reentrance and ultrametricity in three-dimensional Ising spin glasses
Katzgraber, Helmut G.; Thomas, Creighton K.; Hartmann, Alexander K.
2012-02-01
We study the three-dimensional Edwards-Anderson Ising spin glass with bimodal disorder with a fraction of 22.8% antiferromagnetic bonds. Parallel tempering Monte Carlo simulations down to very low temperatures show that for this fraction of antiferromagnetic bonds the phase diagram of the system is reentrant, in agreement with previous results. Furthemore, using a clustering analysis, we analyze the ultrametric properties of phase space for this model.
Kallen Lehman approach to 3D Ising model
Canfora, F.
2007-03-01
A “Kallen-Lehman” approach to Ising model, inspired by quantum field theory à la Regge, is proposed. The analogy with the Kallen-Lehman representation leads to a formula for the free-energy of the 3D model with few free parameters which could be matched with the numerical data. The possible application of this scheme to the spin glass case is shortly discussed.
Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds
Directory of Open Access Journals (Sweden)
V. Ohanyan
2009-01-01
Full Text Available The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground state properties are also investigated, the corresponding ground state phase diagram is presented.
Thermal diode from two-dimensional asymmetrical Ising lattices.
Wang, Lei; Li, Baowen
2011-06-01
Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity κ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.
Exact interface model for wetting in the planar Ising model.
Upton, P J
1999-10-01
At the wetting transition in the two-dimensional Ising model the long contour (interface) gets depinned from the substrate. It is found that on sufficiently large length scales the statistics of the long contour are described by a unique probability measure corresponding to a continuous "interface model" with an interface binding "potential" given by a Dirac delta function supported on the substrate. A lattice solid-on-solid model is shown to give similar results.
Magnetization Profiles of Ferromagnetic Ising Films in a Transverse Field
Institute of Scientific and Technical Information of China (English)
WANG Xiao-Guang; PAN Shao-Hua; YANG Guo-Zhen
2000-01-01
Within the framework of the mean field theory, we study the magnetization profiles of ferromagnetic Ising films in a transverse field. By the transfer matrix method, we first derive a general nonlinear equation for phase transition temperatures and then calculate the magnetization profiles of the system. The method proposed here can be applied to ferromagnetic films with arbitrary surface layer number, bulk layer number, exchange interaction constants and transverse fields.
TBA boundary flows in the tricritical Ising field theory
Energy Technology Data Exchange (ETDEWEB)
Nepomechie, Rafael I. E-mail: nepomechie@physics.miami.edu; Ahn, Changrim
2002-12-30
Boundary S matrices for the boundary tricritical Ising field theory (TIM), both with and without supersymmetry, have previously been proposed. Here we provide support for these S matrices by showing that the corresponding boundary entropies are consistent with the expected boundary flows. We develop the fusion procedure for boundary RSOS models, with which we derive exact inversion identities for the TIM. We confirm the TBA description of nonsupersymmetric boundary flows of Lesage et al. and we obtain corresponding descriptions of supersymmetric boundary flows.
Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics
Ye, J.; Machta, J.; Newman, C. M.; Stein, D L
2013-01-01
Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state ("nature") vs. the realization of the stochastic dynamics ("nurture") in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from $T=\\infty$ to $T=0$. We performed Monte Carlo studies on the overlap between "identical twins" raised in independent dyn...
Coupled modified baker's transformations for the Ising model.
Sakaguchi, H
1999-12-01
An invertible coupled map lattice is proposed for the Ising model. Each elemental map is a modified baker's transformation, which is a two-dimensional map of X and Y. The time evolution of the spin variable is memorized in the binary representation of the Y variable. The temporal entropy and time correlation of the spin variable are calculated from the snapshot configuration of the Y variables.
Yamagata, Atsushi
1994-01-01
We perform the Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, $z_{\\rm c} = 1.0588 \\pm 0.0003$. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.
2007-01-01
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.
Plasma electrons as tracers of distant magnetotail structure - ISEE-3
Baker, D. N.; Bame, S. J.; Gosling, J. T.; Gussenhoven, M. S.
1988-01-01
This paper compares the electron spectra and phase space densities measured concurrently by ISEE-3 at 200 R(E), with those measured by DMSP at low altitudes. The field-aligned lobe electron phase space densities above 200 eV at ISEE were found to agree well with the DMSP-measured polar rain phase space densities near the polar cap; the spectral slopes above 200 eV were also similar. Below 100-200 eV, a thermal electron population was measured by ISEE in the distant tail, which arose from local entry of plasma through the distant magnetopause, which is not present at DMSP altitudes. These data show that the suprathermal tail lobe electrons are essentially a test particle population which can move freely along field lines to form polar rain; in contrast, the thermal electrons are bound to the tailward-flowing lobe ion population far down the tail and, thus, cannot reach the polar cap regions.
The Ising model in physics and statistical genetics.
Majewski, J; Li, H; Ott, J
2001-10-01
Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis.
Ising anyons in frustration-free Majorana-dimer models
Ware, Brayden; Son, Jun Ho; Cheng, Meng; Mishmash, Ryan V.; Alicea, Jason; Bauer, Bela
2016-09-01
Dimer models have long been a fruitful playground for understanding topological physics. Here, we introduce a class, termed Majorana-dimer models, wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological px-i py superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the Ising×(px-i py) theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.
Pan, Xue; Wu, Yuan-Fang
2016-01-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). The order has been calculated to the sixth one at experiments. The corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class with QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that when the critical point is approached from the crossover side, the sixth order cumulant is negative. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising mod...
Pan, Xue; Chen, Li-Zhu; Wu, Yuan-Fang
2016-09-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign. Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)
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.
Directory of Open Access Journals (Sweden)
Aysegul Ates
2016-03-01
Full Text Available Turkey is one of the most dynamic emerging markets in the world and its futures market has developed significantly since the introduction of futures contracts by Turkish Derivatives Exchange in 2005. Istanbul Stock Index 30 (ISE 30 futures was one of the first contracts introduced and its trading increased rapidly over time. This study specifically focuses on the evolution and stability of cointegration relationship between the futures and spot prices of ISE 30 index during the sample period from February 4, 2005 through October 19, 2012. We test whether changing market conditions have an impact on the long-run relationship between spot index and index futures markets by employing recursive and rolling cointegration techniques. The findings reveal that the cointegration relationship weakens significantly during the global financial crisis and eurozone debt crisis periods but holds mostly over the estimation period.
Critical endpoint behavior: A Wang Landau study
Landau, D. P.; Wang, Fugao; Tsai, Shan-Ho
2008-07-01
We study the critical endpoint behavior using an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. The simulation method we use is Wang-Landau sampling in a two-dimensional parameter space. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
"We are all in the same boat" - ISEE leaders' trip to China
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The motto of Tongji University, whose name literallymeans "we are all in the same boat, and must work to-gether to reach common goals", describes the harvest ofISEE leaders' mission to China in May 2007. ISEE Presi-dent Joan Martinez-Alier, President-Elect Peter May andthe society's founder and first President, Robert Costanzaas well as ISEE member Robert Ayres, participated in aseries of events and meetings in Shanghai and Beijing witha view to build institutional collaboration.
Dynamic Critical Behaviour of Wolff's Algorithm for $RP^N$ $\\sigma$-Models
Caracciolo, S.; Edwards, R. G.; Pelissetto, A.; Sokal, A. D.
1992-01-01
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\\sigma$-models. We find that the algorithm in which we update the embedded Ising model \\`a la Swendsen-Wang has critical slowing-down as $z_\\chi \\approx 1$. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain $z_\\chi \\approx 0$. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour ...
Order, disorder, and criticality advanced problems of phase transition theory
Holovatch, Yurij
2004-01-01
This book reviews some of the classic aspects in the theory of phasetransitions and critical phenomena, which has a longhistory. Recently, these aspects are attracting much attention due toessential new contributions. The topics presented in this bookinclude: mathematical theory of the Ising model; equilibrium andnon-equilibrium criticality of one-dimensional quantum spin chains;influence of structural disorder on the critical behaviour of thePotts model; criticality, fractality and multifractality of linkedpolymers; field-theoretical approaches in the superconducting phasetransitions.
Energy Technology Data Exchange (ETDEWEB)
Boughrara, M., E-mail: boughrara_mourad@yahoo.fr; Kerouad, M.; Zaim, A.
2014-06-01
In this work, we have used Monte Carlo Simulation technique (MCS) and effective field theory (EFT) to study the critical and the compensation behaviors of a ferrimagnetic cylindrical nanowire. The system consists of a ferromagnetic spin S{sub A}=1/2 core and a ferromagnetic spin S{sub B}=1 surface shell coupled with an antiferromagnetic interlayer coupling J{sub 1} to the core. The effects of the uniaxial anisotropy, the shell coupling and the interface negative coupling on both the critical and compensation temperatures are investigated. - Highlights: • Phase diagrams and total magnetizations are examined for a ferrimagnetic mixed spin 1/2 and spin 1 Ising nanowire. • The system is studied by effective-field theory and Monte Carlo (MC) simulation. • The effects of the uniaxial anisotropy, the shell coupling and the interface negative coupling on both the critical and compensation temperatures are investigated.
Shabunina, E. V.; Spirin, D. V.; Popov, A. A.; Udodov, V. N.; Potekaev, A. I.
2013-05-01
Using a Monte Carlo simulation, the effect of external field, temperature, system's dimensions and interaction of non-nearest neighbors on the relaxation time and critical indices of an antiferromagnetic-to-ferromagnetic phase transition is investigated taking into account nonmagnetic impurities within a modified, onedimensional, nanosized Ising model. It is shown that the non-equilibrium processes taking place in the magnetic material could be classified as fast and slow, whose velocities differ by more than a thousand times. In the case of fast processes, metastable (including ferromagnetic) states (observed experimentally) are the first to form, while in the case of slow processes the system transits into a stable state. The behavior of the dynamic critical exponent ( z) and static correlation-length critical exponent ( ν) is revealed for the model of a 1D ferromagnetic for the case of arbitrary concentrations of nonmagnetic impurities.
Properties of the interface in the confined Ising magnet with competing surface fields
Energy Technology Data Exchange (ETDEWEB)
Albano, Ezequiel V. [Facultad de Ciencias Exactas, INIFTA: Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas, UNLP, CONICET, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)]. E-mail: ealbano@inifta.unlp.edu.ar; Virgiliis, Andres de [Facultad de Ciencias Exactas, INIFTA: Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas, UNLP, CONICET, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina) and Institut fuer Physik, Johannes Gutenberg Universitaet, WA331, Staudingerweg 7, D-55099 Mainz (Germany); Mueller, Marcus [Institut fuer Physik, Johannes Gutenberg Universitaet, WA331, Staudingerweg 7, D-55099 Mainz (Germany); Institut fuer Theoretische Physik, Georg-August Universitaet, Friedrich Hund Platz 1, 37077 Goettingen (Germany); Binder, Kurt [Institut fuer Physik, Johannes Gutenberg Universitaet, WA331, Staudingerweg 7, D-55099 Mainz (Germany)
2007-02-01
A two-dimensional magnetic Ising system confined in an LxD geometry (L-bar D) in the presence of competing magnetic fields (h) acting at opposite walls along the D-direction, exhibits an interface between domains of different orientation that run parallel to the walls. In the limit L->{approx}, this interface undergoes a wetting transition that occurs at the critical curve T{sub w}(h), so that for T
Break of universality for an Ising model with aperiodic Rudin-Shapiro interactions
Andrade, R. F. S.; Pinho, S. T. R.
2003-08-01
We analyze the ferromagnetic Ising model on non-Euclidean scale invariant lattices with aperiodic interactions ( J A , J B , J C , J D ) defined by Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR) and transfer matrix (TM) techniques. The analysis of the invariant sets of the zero-field MKR transformation indicates that the critical behavior, completely distinct from the one of the uniform model, is described by a new off-diagonal fixed point. This contrasts with other aperiodic models where the new critical behavior is described by a period-two cycle. With the new fixed point, values for the thermal critical exponents, α and ν, as well as the period of log-periodic oscillations, are obtained. Exact recursive maps for all thermodynamical functions are derived within the TM approach. The explicit dependence of the thermodynamical functions with respect to temperature is evaluated by the numerical iteration of the set of maps until a previously chosen convergence is achieved. They also indicate that, depending on the actual choice for the aperiodic coupling constants, the magnetic exponents (β and γ) assume different values. However the Rushbrook relation is always satisfied.
Many-body localization in Ising models with random long-range interactions
Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui
2016-12-01
We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.
Random-field Ising model: Insight from zero-temperature simulations
Directory of Open Access Journals (Sweden)
P.E. Theodorakis
2014-12-01
Full Text Available We enlighten some critical aspects of the three-dimensional (d=3 random-field Ising model (RFIM from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V=LxLxL, where L denotes linear lattice size and Lmax=156. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hmax and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian RFIM at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.
Globally nilpotent differential operators and the square Ising model
Energy Technology Data Exchange (ETDEWEB)
Bostan, A [INRIA Rocquencourt, Domaine de Voluceau, BP 105 78153 Le Chesnay Cedex (France); Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida (Algeria); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, CNRS, Universite de Paris, Tour 24, 4eme etage, Case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Weil, J-A [LACO, XLIM, Universite de Limoges, 123 Avenue Albert Thomas, 87060 Limoges Cedex (France)], E-mail: alin.bostan@inria.fr, E-mail: boukraa@mail.univ-blida.dz, E-mail: maillard@lptmc.jussieu.fr, E-mail: jacques-arthur.weil@unilim.fr, E-mail: njzenine@yahoo.com
2009-03-27
We recall various multiple integrals with one parameter, related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their {lambda}-extensions. The univariate analytic functions defined by these integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations, as well as their Russian-doll and direct sum structures. These differential operators are selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. We also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known. Focusing on the factorized parts of all these operators, we find out that the global nilpotence of the factors (resp. p-curvature nullity) corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, curves of genus five, six,..., and even a remarkable weight-1 modular form emerging in the three-particle contribution {chi}{sup (3)} of the magnetic susceptibility of the square Ising model. Noticeably, this associated weight-1 modular form is also seen in the factors of the differential operator for another n-fold integral of the Ising class, {phi}{sup (3)}{sub H}, for the staircase polygons counting, and in Apery's study of {zeta}(3). G-functions naturally occur as solutions of globally nilpotent operators. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or {infinity}) that correspond to the confluence of singularities in the scaling limit
In-Space Engine (ISE-100) Development - Design Verification Test
Trinh, Huu P.; Popp, Chris; Bullard, Brad
2017-01-01
In the past decade, NASA has formulated science mission concepts with an anticipation of landing spacecraft on the lunar surface, meteoroids, and other planets. Advancing thruster technology for spacecraft propulsion systems has been considered for maximizing science payload. Starting in 2010, development of In-Space Engine (designated as ISE-100) has been carried out. ISE-100 thruster is designed based on heritage Missile Defense Agency (MDA) technology aimed for a lightweight and efficient system in terms volume and packaging. It runs with a hypergolic bi-propellant system: MON-25 (nitrogen tetroxide, N2O4, with 25% of nitric oxide, NO) and MMH (monomethylhydrazine, CH6N2) for NASA spacecraft applications. The utilization of this propellant system will provide a propulsion system capable of operating at wide range of temperatures, from 50 C (122 F) down to -30 C (-22 F) to drastically reduce heater power. The thruster is designed to deliver 100 lb(sub f) of thrust with the capability of a pulse mode operation for a wide range of mission duty cycles (MDCs). Two thrusters were fabricated. As part of the engine development, this test campaign is dedicated for the design verification of the thruster. This presentation will report the efforts of the design verification hot-fire test program of the ISE-100 thruster in collaboration between NASA Marshall Space Flight Center (MSFC) and Aerojet Rocketdyne (AR) test teams. The hot-fire tests were conducted at Advance Mobile Propulsion Test (AMPT) facility in Durango, Colorado, from May 13 to June 10, 2016. This presentation will also provide a summary of key points from the test results.
Interacting damage models mapped onto ising and percolation models
Energy Technology Data Exchange (ETDEWEB)
Toussaint, Renaud; Pride, Steven R.
2004-03-23
The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based
Magnetic configuration of the distant plasma sheet - ISEE 3 observations
Slavin, J. A.; Smith, E. J.; Daly, P. W.; Sanderson, T. R.; Wenzel, K.-P.; Lepping, R. P.
1987-01-01
The influence of the IMF orientation and magnitude and substorm activity on the magnetic configuration of the central plasma sheet at 20-240 earth radii down the geomagnetic tail is investigated on the basis of ISEE-3 data. The results are presented graphically, and high-speed antisolar bulk flows threaded by southward magnetic fields are shown to be present in the distant plasma sheet after periods of substorm activity and southward IMF Bz. The effective dayside reconnection efficiency is estimated as 25 + or - 4 percent, in good agreement with theoretical models.
ISEE 3 observations of plasmoids with flux rope magnectic topologies
Slavin, J.; Owen, C.; KUZNETSOVA, M.
1995-01-01
This paper reports new evidence for the existence of plasmoids with force‐free flux rope magnetic topologies. Motivated by the fact that force‐free magnetic flux ropes have intense axial fields at their centers, the ISEE 3 observations have been searched for plasma sheet intervals in which the magnetic field intensity exceeds that in the lobes by ≥10% for a minute or longer. A total of 39 “high field regions” were found which met this simple criterion. Further examination showed that they nea...
Dynamical TAP equations for non-equilibrium Ising spin glasses
DEFF Research Database (Denmark)
Roudi, Yasser; Hertz, John
2011-01-01
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......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...
Complete wetting in the three-dimensional transverse Ising model
Harris, A. B.; Micheletti, C.; Yeomans, J. M.
1996-08-01
We consider a three-dimensional Ising model in a transverse magnetic field h and a bulk field H. An interface is introduced by an appropriate choice of boundary conditions. At the point ( H=0, h=0) spin configurations corresponding to different positions of the interface are degenerate. By studying the phase diagram near this multiphase point using quantum mechanical perturbation theory, we show that the quantum fluctuations, controlled by h, split the multiphase degeneracy giving rise to an infinite sequence of layering transitions.
Corner wetting transition in the two-dimensional Ising model
Lipowski, Adam
1998-07-01
We study the interfacial behavior of the two-dimensional Ising model at the corner of weakened bonds. Monte Carlo simulations results show that the interface is pinned to the corner at a lower temperature than a certain temperature Tcw at which it undergoes a corner wetting transition. The temperature Tcw is substantially lower than the temperature of the ordinary wetting transition with a line of weakened bonds. A solid-on-solid-like model is proposed, which provides a supplementary description of the corner wetting transition.
Fluctuation dissipation ratio in the one dimensional kinetic Ising model
Lippiello, E.; Zannetti, M.
2000-01-01
The exact relation between the response function $R(t,t^{\\prime})$ and the two time correlation function $C(t,t^{\\prime})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\\prime})$ is found to depend on time through $C(t,t^{\\prime})$ in the time region where scaling $C(t,t^{\\prime}) = f(t/t^{\\prime})$ holds. The crossover from the nontrivial form $X(C(t,t^{\\prime}))$ to $X(t,t^{\\prime}) \\equiv 1$ t...
Non-Abelian anyons: when Ising meets Fibonacci.
Grosfeld, E; Schoutens, K
2009-08-14
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 theory with a central charge c=7/10. We discuss effects of the mismatch of the quantum statistical properties of the quasiholes between the two sides, as reflected by the interface theory.
Ising model simulation in directed lattices and networks
Lima, F. W. S.; Stauffer, D.
2006-01-01
On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.
Simulation of financial market via nonlinear Ising model
Ko, Bonggyun; Song, Jae Wook; Chang, Woojin
2016-09-01
In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.
Magnetic properties of a single transverse Ising ferrimagnetic nanoparticle
Energy Technology Data Exchange (ETDEWEB)
Bouhou, S.; El Hamri, M. [Laboratoire de Physique des Matériaux et Modélisation des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Essaoudi, I. [Laboratoire de Physique des Matériaux et Modélisation des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden); Ainane, A., E-mail: ainane@pks.mpg.de [Laboratoire de Physique des Matériaux et Modélisation des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden); Ahuja, R. [Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden)
2015-01-01
Using the effective field theory with a probability distribution technique that accounts for the self-spin correlation function, the thermal and the magnetic properties of a single Ising nanoparticle consisting of a ferromagnetic core, a ferromagnetic surface shell and a ferrimagnetic interface coupling are examined. The effect of the transverse field in the surface shell, the exchange interactions between core/shell and in surface shell on the free energy, thermal magnetization, specific heat and susceptibility are studied. A number of interesting phenomena have been found such as the existence of the compensation phenomenon and the magnetization profiles exhibit P-type, N-type and Q-type behaviors.
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
Entanglement in Ising Chain with Inhomogeneous Magnetic Field
Institute of Scientific and Technical Information of China (English)
Cenk Akyüz; Ekrem Aydmer
2008-01-01
We have numerically calculated the thermal entanglement of a two-qubit system at low temperatures in a isotropic Ising chain under an inhomogeneous magnetic field.It is shown that in the homogeneous magnetic field,the twoqubit system has entangled states.It is concluded that the presence of the inhomogeneity in the magnetic field plays an effective role on the entangled states.Finally,it is suggested that the inhomogeneity in the magnetic field can be used to create two separated entangled formations in a two-qubit system.
Modified Mean Field approximation for the Ising Model
Di Bartolo, Cayetano
2009-01-01
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.
A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
Wang, Zhe; Marandi, Alireza; Wen, Kai; Byer, Robert L.; Yamamoto, Yoshihisa
2014-03-01
A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network. This project is supported by the FIRST program of Japanese Government. Zhe Wang is also grateful for the support from Stanford Graduate Fellowship.
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.
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-10-10
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.
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-10-01
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.
Corner wetting in the two-dimensional Ising model: Monte Carlo results
Energy Technology Data Exchange (ETDEWEB)
Albano, E V [INIFTA, Universidad Nacional de La Plata, CC 16 Suc. 4, 1900 La Plata (Argentina); Virgiliis, A De [INIFTA, Universidad Nacional de La Plata, CC 16 Suc. 4, 1900 La Plata (Argentina); Mueller, M [Institut fuer Physik, Johannes Gutenberg Universitaet, Staudinger Weg 7, D-55099 Mainz (Germany); Binder, K [Institut fuer Physik, Johannes Gutenberg Universitaet, Staudinger Weg 7, D-55099 Mainz (Germany)
2003-01-29
Square LxL (L=24-128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature T{sub c} of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T{sub f} (h) runs from the upper left corner to the lower right corner, while for T
Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution
Institute of Scientific and Technical Information of China (English)
Sudha; B. G. Divyamani; A. R. Usha Devi
2011-01-01
Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically we show that among 4-qubit states obeying exchange symmetry, all states except W class (and their linear combination) lose their symmetry under time evolution with Ising Hamiltonian. Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits, we indicate that all N-qubit states (N ＞ 5) obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.%@@ Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry, all states except W class (and their linear combination) lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits, we indicate that all N-qubit states (N > 5) obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
A version of the two-dimensional site-diluted spin-(1/2 Ising model is proposed as a microscopic interaction model which governs solidification and growth processes controlled by vacancy diffusion. The Ising Hamiltonian describes a solid-fluid phase transition and it permits a thermodynamic......-water interfaces....
Energy Technology Data Exchange (ETDEWEB)
Candia, Julian; Albano, Ezequiel V.
2001-06-01
The magnetic Eden model (MEM) [N. Vandewalle and M. Ausloos, Phys. Rev. E >50, R635 (1994)] with ferromagnetic interactions between nearest-neighbor spins is studied in (d+1)-dimensional rectangular geometries for d=1,2. In the MEM, magnetic clusters are grown by adding spins at the boundaries of the clusters. The orientation of the added spins depends on both the energetic interaction with already deposited spins and the temperature, through a Boltzmann factor. A numerical Monte Carlo investigation of the MEM has been performed and the results of the simulations have been analyzed using finite-size scaling arguments. As in the case of the Ising model, the MEM in d=1 is noncritical (only exhibits an ordered phase at T=0). In d=2 the MEM exhibits an order-disorder transition of second order at a finite temperature. Such transition has been characterized in detail and the relevant critical exponents have been determined. These exponents are in agreement (within error bars) with those of the Ising model in two dimensions. Further similarities between both models have been found by evaluating the probability distribution of the order parameter, the magnetization, and the susceptibility. Results obtained by means of extensive computer simulations allow us to put forward a conjecture that establishes a nontrivial correspondence between the MEM for the irreversible growth of spins and the equilibrium Ising model. This conjecture is certainly a theoretical challenge and its confirmation will contribute to the development of a framework for the study of irreversible growth processes.
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
Giant magnetocaloric effect, magnetization plateaux and jumps of the regular Ising polyhedra
Energy Technology Data Exchange (ETDEWEB)
Strečka, Jozef, E-mail: jozef.strecka@upjs.sk [Institute of Physics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia); Karľová, Katarína [Institute of Physics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia); Madaras, Tomáš [Institute of Mathematics, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01 Košice (Slovakia)
2015-06-15
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.
A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems
Takata, Kenta; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa
2016-01-01
Many tasks in modern life, such as efficient traveling, image processing and integrated circuit optimization, are modeled as complex combinatorial optimization problems. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine with a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6 % of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multimode dynamics of femtosecond pulses can improve its ...
Institute of Scientific and Technical Information of China (English)
罗孟波; 陈庆虎; 焦正宽
2002-01-01
We investigate the influence of the boundary condition on the short-time dynamic behaviour of the Ising-like phase transition in square-lattice fully frustrated (FF) XY models with periodic and fluctuating twist boundary conditions. The transition temperature Tc and the dynamic and static critical exponents z, 2β/v and v are estimated for both cases using short-time dynamic scaling analysis. The results show that both models have the same critical exponents, indicating that the boundary condition has nearly no effect on the short-time dynamic behaviour of the FFXY model.
Directory of Open Access Journals (Sweden)
M.P. Kozlovskii
2010-01-01
Full Text Available The present work is devoted to the investigation of the 3D Ising-like model in the presence of an external field in the vicinity of critical point. The method of collective variables is used. General expressions for the order parameter and susceptibility are calculated as functions of temperature and the external field as well as scaling functions of that are explicitly obtained. The results are compared with the ones obtained within the framework of parametric representation of the equation of state and Monte Carlo simulations. New expression for the exit point from critical regime of the order parameter fluctuations is proposed and used for the calculation.
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.
Equation of State and Thermodynamic Functions of the Ising-like Magnet at $T>T_c$
Kozlovskii, Miroslaw P
2006-01-01
The 3D Ising-like system in the external field is described using the non-perturbative collective variables method. The universal as well as nonuniversal system characteristics are obtained within the framework of this approach. The calculations are carried out on the microscopic level starting from the Hamiltonian. They are valid in the whole $h-T$ plane of the critical region. It is established, that the contributions related with wave vector values $\\vk\\to0$ exhibit the properties of the total system near the critical point. The behaviour of the susceptibility as function of the temperature in the presence of the field is investigated. The locations of the maximums susceptibility on the temperature scale for different values of the field are established.
Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition
Halder, Ajay; Acharyya, Muktish
2016-12-01
The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the direction x. We have detected two main dynamical phases namely, pinned and oscillating spin clusters. Depending on the value of field amplitude the system is found to undergo a phase transition from oscillating spin cluster to pinned as the system is cooled down. The time averaged magnetisation over a full cycle of magnetic field oscillations is defined as the dynamic order parameter. The transition is detected by studying the temperature dependences of the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The dependence of the transition temperature on the magnetic field amplitude and on the wavelength of the magnetic field wave is studied at a single frequency. A comprehensive phase boundary is drawn in the plane described by the temperature and field amplitude for two different wavelengths of the magnetic wave. The variation of instantaneous line magnetisation during a period of magnetic field oscillation for standing wave mode is compared to those for the propagating wave mode. Also the probability that a spin at any site, flips, is calculated. The above mentioned variations and the probability of spin flip clearly distinguish between the dynamical phases formed by propagating magnetic wave and by standing magnetic wave in an Ising ferromagnet.
High spacecraft potentials on ISEE-1 in sunlight
Energy Technology Data Exchange (ETDEWEB)
Whipple, E.C.; Olsen, R.C.
1987-01-01
Data from the two electric-field experiments and from the plasma-composition experiment on ISEE-1 show that the spacecraft charged to close to -70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron-spectrometer experiment show that there was a potential barrier of some -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of space charge. The stringent electrostatic cleanliness specifications imposed on ISEE made by the presence of differential charging seem unlikely, if these precautions were effective. Modeling of this event to determine if the barrier was produced by the presence of space charge, suggested that this could not explain the observed barrier. The angular shape of the distribution could be successfully modeled as a product of differential charging on the solar arrays. This implies that the conductive coating was not completely effective in preventing differential charging, and that differential charging did occur.
Neutral sheet crossings by ISEE-3 in the distant magnetotail
Heikkila, W. J.; Slavin, J. A.; Smith, E. J.; Baker, D. N.; Zwickl, R. D.
1986-01-01
The magnetic field data from ISEE-3 in the distant magnetotail at crossings of the field reversal (or neutral sheet) region are analyzed to determine the instantaneous direction of the normal component B(z) at the crossing. Crossings in the middle of the aberrated magnetotail near the apogee A2 of the first deep-tail orbit of ISEE-3 in January-February, 1983 were selected. Data for an interval of one hour is discussed at length to illustrate some of the difficulties that can occur. One particular smooth crossing at 15:56 UT, February 4, 1983, shows that complicated microstructure can occur in times shorter than one minute; averaging over long times may eliminate essential information for this purpose. By inspecting the magnetic field data at the highest resolution, however, it is shown that the direction of the plasma sheet flows and the sense of B(z) across the neutral sheet do not always agree with the reconnection models. Rather, they indicate that the low latitude boundary layer may play a significant role in the dynamics of the magnetotail.
Nonequilibrium relaxation study of Ising spin glass models
Ozeki, Yukiyasu; Ito, Nobuyasu
2001-07-01
As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The +/-J Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of L=127 and for four-dimensional (hypercubic) lattice up to L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) Q(t,tw)≡[F], which is a spin correlation of two replicas produced after the waiting time tw from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development (t>>tw) in the SG phase. This provides a reliable upper bound of the transition temperature Tg. It is also found that a scaling relation, Q(t,tw)=t-λqwq¯(t/tw), holds just around the transition point providing the lower bound of Tg. Together with these two bounds, we propose a new dynamical way for the estimation of Tg from much larger systems. In the SG phase, the power-law behavior of the CCF for t>>tw suggests that the SG phase in short-range Ising models has a rugged phase space.
Oscillating hysteresis in the q-neighbor Ising model.
Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition.
THE EFFECT OF INVESTOR SENTIMENT ON ISE SECTOR INDICES
Directory of Open Access Journals (Sweden)
SERPİL CANBAŞ
2013-06-01
Full Text Available Determining the factors that affect stock returns is one of the most investigated topics of the finance literature. A number of models have been developed to explain stock returns. Some of these models maintain that stock returns are generated rationally. These models are, Capital Asset Pricing Model, Index Models, Arbitrage Pricing Model and Macroeconomic Factor Models. Nevertheless, these models could not have explained stock returns, although they have used different parameters and methods. Some studies have maintained that investor psychology would have a role in the stock return generation process. There are three theories that investigate the effect of investor psychology on financial markets: Mental accounting theory, herd behavior theory and investor sentiment theory. The aim of this study is to investigate the effect of investor sentiment on stock returns. In this context, three investor sentiment proxies have been determined in the light of previous studies. These proxies are closed-end fund discount, average fund flow of mutual funds and the ratio of net stock purchases of foreign investors to ISE market capitalization. ISE sector indices are used to proxy stock returns. On the other hand, there is a possibility that investor sentiment would merely reflect economic innovations. Some economic factors are used as control variables in order to examine this possibility. Regression analyses are employed for investigating the effect of investor sentiment on stock returns. Findings suggest that investor sentiment affect stock returns systematically. This finding keeps its robustness when economic variables are added to the model.
Žukovič, Milan; Tomita, Yusuke; Kamiya, Y.
2017-07-01
We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling JA and the ferromagnetic (FM) one JB for the respective layers, which are coupled by the interlayer interaction JAB by using Monte Carlo simulations. When JA and JB are of the same order, the unfrustrated FM plane orders first at a high temperature Tc 1˜JB . The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below Tc 2. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-type pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in ∝JA/T is controlled by a line of Gaussian fixed points at T =0 . In the crossover region, a continuous variation in the effective critical exponent 4/9 ≲ηeff≲1/2 is observed. The phase diagram by changing the ratio JA/JB is also investigated.
Albano, Ezequiel V.; DeVirgiliis, Andres; Müller, Marcus; Binder, Kurt
2004-06-01
Confined magnetic Ising films in a L × D geometry (L \\ll D ), with short-range competing magnetic fields (h) acting at opposite walls along the D-direction, exhibit a slightly rounded localization-delocalization transition of the interface between domains of different orientations that runs parallel to the walls. This transition is the precursor of a wetting transition that occurs in the limit of infinite film thickness (L \\to \\infty ) at the critical curve Tw(h). For TTw(h)) such an interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is freely fluctuating around the centre of the film. Starting from disordered configurations, corresponding to T=\\infty , we quench to the wetting critical temperature and study the dynamics of the approach to the stationary regime by means of extensive Monte Carlo simulations. It is found that for all layers parallel to the wall (rows), the row magnetizations exhibit a peak at a time \\tau _{\\max } \\propto L^{2} and subsequently relax to the stationary, equilibrium behaviour. The characteristic time for such a relaxation scales as \\tau_{\\mathrm {R}} \\propto L^{4} , as expected from theoretical arguments, that are discussed in detail.
Milchev, A; Müller, M; Binder, K
2005-09-01
The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/-H(s) is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bipyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L --> infinity) at the temperature Tf(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a susceptibility that diverges with a Curie-Weiss power law, when the transition is approached from either side. A Landau theory with size-dependent critical amplitudes is proposed to explain these observations, and confirmed by finite size scaling analysis of the simulation results. The extension of these results to other nanosystems (gas-liquid systems, binary mixtures, etc.) is briefly discussed.
Monte Carlo study of the Ising ferromagnet on the site-diluted triangular lattice
Najafi, M. N.
2016-01-01
In this paper we consider the Ising model on the triangular percolation lattice and analyze its geometrical interfaces and spin clusters. The (site) percolation lattice is tuned by the occupancy parameter p which is the probability that a site is magnetic. Some statistical observables are studied in terms of temperature (T) and p. We find two separate (second order) transition lines, namely magnetic and percolation transition lines. The finite size analysis shows that the magnetic transition line is a critical one with varying exponents, having its root in the fact that the line is composed of individual critical points, or that a cross-over occurs between two (UV and IR) fixed points. For the percolation transition line however the exponents seem to be identical. Schramm-Loewner evolution (SLE) is employed to address the problem of conformal invariance at the points on the magnetic transition line. We find that at p ≃ 0.9 the model is described by κ ≃ 4 whose corresponding central charge is maximum with respect to the others.
Cornfeld, Eyal; Sela, Eran
2017-08-01
The entanglement entropy in one-dimensional critical systems with boundaries has been associated with the noninteger ground-state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well-known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an n -sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing one to track in real space the presence of a region containing one-half of a qubit with entropy 1/2 log(2 ) , associated with a free local Majorana fermion.
Has the QCD critical point been observed at RHIC?
Antoniou, N G; Diakonos, F K
2016-01-01
The experimental search for the location of the QCD critical point in the phase diagram is of primary importance. In a recent publication it is claimed that measurements at RHIC lead not only to the location of the critical point ($\\mu_{cep}=95$ MeV, $T_{cep}=165$ MeV) but also to the verification of its universality class ($3d$ Ising system) by extracting the values of the critical exponents ($\\gamma=1.2$, $\
The Simulation Software of Semiconductor Device ISE-TCAD%半导体器件模拟软件ISE-TCAD
Institute of Scientific and Technical Information of China (English)
袁博; 陈世彬
2012-01-01
本文的研究目的是对半导体模拟软件ISE-TCAD进行详细介绍,旨在介绍软件的模拟方法,并利用仿真软件ISE-TCAD对其在室温下的正向伏安特性与反向伏安特性进行了模拟仿真,并取得了有价值的数据.从模拟图的结果可知室温(303K)且偏压较低时,电流随着电压呈指数关系增长,W/SiC肖特基势垒二极管的开启电压约为0.2V;偏压较高时,电流增加缓慢,串联电阻效应明显.模拟值表明反向电流数值比正向数值小几个数量级.
Dynamic Critical Behaviour of Wolff's Algorithm for $RP^N$ $\\sigma$-Models
Caracciolo, Sergio; Pelissetto, A; Sokal, A D
1992-01-01
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\\sigma$-models. We find that the algorithm in which we update the embedded Ising model \\`a la Swendsen-Wang has critical slowing-down as $z_\\chi \\approx 1$. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain $z_\\chi \\approx 0$. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.
Criticality in Plasma Membranes
Machta, Benjamin; Papanikolaou, Stefanos; Sethna, James; Veatch, Sarah
2011-03-01
We are motivated by recent observations of micron-sized critical fluctuations in the 2d Ising Universality class in plasma membrane vesicles that are isolated from cortical cytoskeleton. We construct a minimal model of the plasma membrane's interaction with intact cytoskeleton which explains why large scale phase separation has not been observed in Vivo. In addition, we use analytical techniques from conformal field theory and numerical simulations to investigate the form of effective forces mediated by the membrane's proximity to criticality. We show that the range of this force is maximized near a critical point and we quantify its usefulness in mediating communication using techniques from information theory. Finally we use theoretical techniques from statistical physics in conjunction with Monte-Carlo simulations to understand how criticality can be used to increase the efficiency of membrane bound receptor mediated signaling. We expect that this sort of analysis will be broadly useful in understanding and quantifying the role of lipid ``rafts'' in a wide variety of membrane bound processes. Generally, we demonstrate that critical fluctuations provide a physical mechanism to organize and spatially segregate membrane components by providing channels for interaction over relatively large distances.
New method for determination of critical parameters
Ruge, C.; Dunkelmann, S.; Wagner, F.
1992-10-01
Our method uses topological properties of the large clusters in the single-cluster algorithm of Wolff for Monte Carlo simulations of spin systems. We have applied this method to the d=3 Ising model with film geometry near the special transition. As a test for the method we determined the bulk critical temperature and the critical indices in fair agreement with the results obtained by other methods. The new results refer to the critical surface coupling J1c/J=1.5004(20) and the surface exponents, where φ=0.461(15) and βmi=0.237(5).
Magnetismo de superficie em sistemas compressiveis de Ising
Moreira,Antonio Flavio Barbosa
1991-01-01
Dissertação (mestrado) - Universidade Federal de Santa Catarina. Centro de Ciencias Fisicas e Matematicas Neste trabaho estudamos o modelo de Ising em uma rede cúbica semi-infinita. Consideramos um modelo magneto-elástico com uma pressão uniaxial, onde os íons vibram somente em uma direção perpendicular aos planos cristalinos. Na aproximação de campo médio determinamos o diagrama de fases para os acoplamentos críticos de superfície em função da pressão, e o perfil da magnetização. Utiliza...
Propagation of fluctuations in the quantum Ising model
Navez, P.; Tsironis, G. P.; Zagoskin, A. M.
2017-02-01
We investigate entanglement dynamics and correlations in the quantum Ising model in arbitrary dimensions using a large-coordination-number expansion. We start from the pure paramagnetic regime obtained through zero spin-spin coupling and subsequently turn on the interspin interaction in a time-dependent fashion. We investigate analytically and compare results for both the slow adiabatic onset of the interactions and the fast instantaneous switching. We find that in the latter case of an initial excitation mode a quantum correlation wave spreads through the system, propagating with twice the group velocity of the linearized equilibrium modes. This wave establishes the spatiotemporal regime of entangled quantum properties of the system for time scales shorter than the decoherence time and thus provides an indicator for the "quantumness" of the physical system that the specific system models.
The Gonihedric Paradigm Extensions of the Ising Model
Savvidy, George
2015-01-01
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analysed. The model can also be formulated as a spin system with identical partition function. The spin system represents a generalisation of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the tree-dimensional statistical spin system. In three and four dimensions the system exhibits the second order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.
Partition function zeros of an Ising spin glass
Damgaard, P H
1995-01-01
We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched averages. This study is motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization flows in such models with frustration, and by the possible connection of the latter with spin glass behaviour. In any finite volume, the simultaneous distribution of the zeros of all partition functions can be viewed as part of the more general problem of finding the location of all the zeros of a certain class of random polynomials with positive integer coefficients. Some aspects of this problem have been studied in various branches of mathematics, and we show how polynomial mappings which are used in graph theory to classify graphs, may help in characterizing the distribution of zeros. We finally discuss the ...
Bootstrapping Mixed Correlators in the 3D Ising Model
Kos, Filip; Simmons-Duffin, David
2014-01-01
We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a $\\mathbb{Z}_2$ global symmetry. For the leading $\\mathbb{Z}_2$-odd operator $\\sigma$ and $\\mathbb{Z}_2$-even operator $\\epsilon$, we obtain numerical constraints on the allowed dimensions $(\\Delta_\\sigma, \\Delta_\\epsilon)$ assuming that $\\sigma$ and $\\epsilon$ are the only relevant scalars in the theory. These constraints yield a small closed region in $(\\Delta_\\sigma, \\Delta_\\epsilon)$ space compatible with the known values in the 3D Ising CFT.
On truncated generalized Gibbs ensembles in the Ising field theory
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2017-01-01
We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green’s function G(x)= of the complex fermion field \\psi (x) . We find that both truncated GGEs are able to recover G(x), but for a given number of charges the semi-local version performs better.
Interfaces in driven Ising models: shear enhances confinement.
Smith, Thomas H R; Vasilyev, Oleg; Abraham, Douglas B; Maciołek, Anna; Schmidt, Matthias
2008-08-08
We use a phase-separated driven two-dimensional Ising lattice gas to study fluid interfaces exposed to shear flow parallel to the interface. The interface is stabilized by two parallel walls with opposing surface fields, and a driving field parallel to the walls is applied which (i) either acts locally at the walls or (ii) varies linearly with distance across the strip. Using computer simulations with Kawasaki dynamics, we find that the system reaches a steady state in which the magnetization profile is the same as that in equilibrium, but with a rescaled length implying a reduction of the interfacial width. An analogous effect was recently observed in sheared phase-separated colloidal dispersions. Pair correlation functions along the interface decay more rapidly with distance under drive than in equilibrium and for cases of weak drive, can be rescaled to the equilibrium result.
Dynamic specific heat of frustrated Ising spin rings
Ismail, G
2003-01-01
The dynamic specific heat C(omega) is calculated exactly for rings of six coupled Ising spins within Glauber dynamics. We used the response of the internal energy to small temperature oscillations to find C(omega). The spin glass (SG) and disordered ferromagnetic (DFM) rings showed here have four energy minima and thus four diverging relaxation times in the time evolution of magnetization and three such times in the evolution of energy. The properties of the real and imaginary parts of dynamic specific heat are investigated for different temperatures and frequencies. The dynamic susceptibility is affected by the longest relaxing mode while the dynamic specific heat is not. Our results confirm that C(omega) is sensitive only to rapidly relaxing processes for ferromagnetic (FM) and anti-ferromagnetic (AFM) cases. (Author)
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, Tibor; Collura, Mario; Kormos, Márton; Takács, Gábor
2016-01-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while...
Entanglement entropy in a periodically driven Ising chain
Russomanno, Angelo; Santoro, Giuseppe E.; Fazio, Rosario
2016-07-01
In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period τ. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value τ-periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a generalized Gibbs ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state.
Detecting multi-spin interactions in the inverse Ising problem
Albert, Joseph; Swendsen, Robert H.
2017-10-01
While the usual goal in Monte Carlo (MC) simulations of Ising models is the efficient generation of spin configurations with Boltzmann probabilities, the inverse problem is to determine the coupling constants from a given set of spin configurations. Most recent work has been limited to local magnetic fields and pair-wise interactions. We have extended solutions to multi-spin interactions, using correlation function matching (CFM). A more serious limitation of previous work has been the uncertainty of whether a chosen set of interactions is capable of faithfully representing real data. We show how our confirmation testing method uses an additional MC simulation to detect significant interactions that might be missing in the assumed representation of the data.
Modeling dark energy through an Ising fluid with network interactions
Luongo, Orlando
2013-01-01
We show that the dark energy effects can be modeled by using an \\emph{Ising perfect fluid} with network interactions, whose low redshift equation of state, i.e. $\\omega_0$, becomes $\\omega_0=-1$ as in the $\\Lambda$CDM model. In our picture, dark energy is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding equation of state mimics the effects of a variable dark energy term, whose limiting case reduces to the cosmological constant $\\Lambda$. This permits us to avoid the introduction of a vacuum energy as dark energy source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia, baryonic acoustic oscillation and cosmic microwave background measurements. Finally, we perform the AIC and BIC selection criteria, showing t...
Small-world phenomena in physics: the Ising model
Energy Technology Data Exchange (ETDEWEB)
Gitterman, M. [Department of Physics, Bar-Ilan University, Ramat-Gan (Israel)
2000-12-01
The Ising system with a small fraction of random long-range interactions is the simplest example of small-world phenomena in physics. Considering the latter both in an annealed and in a quenched state we conclude that: (a) the existence of random long-range interactions leads to a phase transition in the one-dimensional case and (b) there is a minimal average number p of these interactions per site (p<1 in the annealed state, and p{approx_equal}1 in the quenched state) needed for the appearance of the phase transition. Note that the average number of these bonds, pN/2, is much smaller than the total number of bonds, N{sup 2}/2. (author)
Maximum caliber inference and the stochastic Ising model
Cafaro, Carlo; Ali, Sean Alan
2016-11-01
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.
Energetic particle sounding of the magnetospheric cusp with ISEE-1
Directory of Open Access Journals (Sweden)
K. E. Whitaker
2007-06-01
Full Text Available Observations on 30 October 1978 show the ISEE-1 spacecraft passing though the high-altitude dayside northern magnetospheric cusp region from roughly 16:00 to 18:30 UT, during a slow solar wind period (~380 km/s. More than two orders of magnitude enhancements of the cusp energetic particle (CEP fluxes were observed along with a depressed and turbulent local magnetic field. The observed variations of the pitch angle distributions (PAD provide a unique opportunity to determine the structure of the cusp and the origin of the CEP. Through a boundary sounding technique, the location and orientation of the cusp poleward (or backside boundary was observed for almost 10 min during which time it appeared initially to be stationary in the GSM/GSE X-direction and then moved sunward about 0.12 Earth radii (R_{E}. The orientation remained approximately perpendicular to the GSM/GSE X-axis until it was observed to rotate by 60 degrees in ~3 min before ISEE-1 was fully inside the cusp cavity. The cavity itself was filled with CEP fluxes displaying large anisotropies, indicative of their source being located below (Earthward of the satellite location. The spacecraft entered from the backside of the cusp, then traveled ~4 R_{E} through the cavity, and exited through the "top" of the cavity leaving a region of energetic ions below. The PADs demonstrate that the bow shock cannot be the main source of the observed CEPs. The CEP fluxes were measured at about 8.5 h MLT when the IMF had both an 8–10 nT duskward and southward component.
Nonequilibrium stationary states and phase transitions in directed Ising models
Godrèche, Claude; Bray, Alan J.
2009-12-01
We study the nonequilibrium properties of directed Ising models with non-conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the two-dimensional square lattice; (iii) the two-dimensional triangular lattice and (iv) the three-dimensional cubic lattice. We raise and answer the question: (a) under what conditions is the stationary state described by the equilibrium Boltzmann-Gibbs distribution? We show that, for models (i), (ii) and (iii), in which each spin 'sees' only half of its neighbours, there is a unique set of transition rates, namely with exponential dependence in the local field, for which this is the case. For model (iv), we find that any rates satisfying the constraints required for the stationary measure to be Gibbsian should satisfy detailed balance, ruling out the possibility of directed dynamics. We finally show that directed models on lattices of coordination number z>=8 with exponential rates cannot accommodate a Gibbsian stationary state. We conjecture that this property extends to any form of the rates. We are thus led to the conclusion that directed models with Gibbsian stationary states only exist in dimensions one and two. We then raise the question: (b) do directed Ising models, augmented by Glauber dynamics, exhibit a phase transition to a ferromagnetic state? For the models considered above, the answers are open problems, with the exception of the simple cases (i) and (ii). For Cayley trees, where each spin sees only the spins further from the root, we show that there is a phase transition provided the branching ratio, q, satisfies q>=3.
Institute of Scientific and Technical Information of China (English)
陆星; 蔡静; 张伟
2012-01-01
In the statistical model, the efficiency of most Monte Carlo algorithm reduces quickly near the critical point. In the analysis of traditional local algorithms, a GPU-based parallel simulation algorithm on the triangular lattice Ising model, which greatly improves the efficiency of the Monte Carlo simulation, is raised. For the model with the size of 1 024 X 1 024, a speedup of 69 is achieved. Besides, the critical behavior is analyzed, a high-precision critical point (/Jc = 0.274 66( 1) ) and critical exponents (y, = 1.01(2), yh= 1. 875 6(3) ) of triangular lattice Ising model are obtained, which implies the effectiveness of the GPU algorithm.%在分析传统Monte Carlo算法的基础上,针对三角晶格Ising模型提出了一种基于GPU的并行模拟方法,大大提高了算法的效率.对1 024×1 024的模型,实现了69倍的加速比.通过该算法所得数据分析模型的临界行为,获得了高精度的临界点βc=0.27466(1)和临界指数y1=1.01(2),yh=1.875 6(3).
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.
Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field
Institute of Scientific and Technical Information of China (English)
Khalid Bannora; Galal Ismail; Wafaa Hassan
2011-01-01
The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance = H2RF is considered. The free-energy (F), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (X) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.
Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field
Magalhães, S. G.; Zimmer, F. M.; Morais, C. V.
2009-06-01
The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ± indicate instability problems for the SG solution close to all ranges of a first order boundary.
Trobo, Marta L.; Albano, Ezequiel V.; Binder, Kurt
2016-05-01
As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b , where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature Tw of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T . Also, precursor effects to droplet formation as T approaches Tw from below are studied. In accord with theoretical predictions, for T >Tw the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b1 /2). So, the area of the droplet is proportional to b3 /2, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.
Square lattice Ising model {chi}-tilde{sup (5)} ODE in exact arithmetic
Energy Technology Data Exchange (ETDEWEB)
Nickel, B [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Jensen, I; Guttmann, A J [ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010 (Australia); Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida, Blida (Algeria); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M, E-mail: bgn@physics.uoguelph.c, E-mail: I.Jensen@ms.unimelb.edu.a, E-mail: boukraa@mail.univ-blida.d, E-mail: tonyg@ms.unimelb.edu.a, E-mail: maillard@lptmc.jussieu.f, E-mail: njzenine@yahoo.co [LPTMC, UMR 7600 CNRS, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2010-05-14
We obtain in exact arithmetic the order 24 linear differential operator L{sub 24} and the right-hand side E{sup (5)} of the inhomogeneous equation L{sub 24}({Phi}{sup (5)}) = E{sup (5)}, where {Phi}{sup (5)}={chi}-tilde{sup (5)}-{chi}-tilde{sup (3)}/2+{chi}-tilde{sup (1)}/120 is a linear combination of n-particle contributions to the susceptibility of the square lattice Ising model. In Bostan et al (2009 J. Phys. A: Math. Theor. 42 275209), the operator L{sub 24} (modulo a prime) was shown to factorize into L{sub 12}{sup (left){center_dot}}L{sub 12}{sup (right)}; here we prove that no further factorization of the order 12 operator L{sub 12}{sup (left)} is possible. We use the exact ODE to obtain the behaviour of {chi}-tilde{sup (5)} at the ferromagnetic critical point and to obtain a limited number of analytic continuations of {chi}-tilde{sup (5)} beyond the principal disc defined by its high temperature series. Contrary to a speculation in Boukraa et al (2008 J. Phys. A: Math. Theor. 41 455202), we find that {chi}-tilde{sup (5)} is singular at w = 1/2 on an infinite number of branches.
A study of the bilayer Bethe lattice for spin-32 Ising model
Energy Technology Data Exchange (ETDEWEB)
Albayrak, Erhan [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)]. E-mail: albayrak@erciyes.edu.tr; Yilmaz, Saban [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Akkaya, Seyma [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2007-03-15
The spin-32 Ising model on the bilayer Bethe lattice is studied in terms of the exact recursion relations with the intralayer bilinear interactions J{sub 11} and J{sub 22} of the two layers with ferromagnetic coupling and interlayer bilinear interaction J{sub 12} between the layers with ferromagnetic or antiferromagnetic coupling. We first have obtained the ground state configurations of the model on the (J{sub 22}/vertical barJ{sub 11}vertical bar,J{sub 12}/qvertical barJ{sub 11}vertical bar) planes for J{sub 11}<0 and J{sub 11}>0. Then the thermal behaviors of the order-parameters, the total and staggered magnetizations of the two layers and also the spin-spin correlation function between the nearest-neighbor spins of the adjacent layers, are studied to obtain the phase diagrams of the model on the (kT/J{sub 11},J{sub 12}/J{sub 11}) plane for given values of J{sub 22}/J{sub 11} and the coordination number q. As a result, a few types of the critical temperatures of the model are obtained.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Finite size scaling RG: detailed description and applications to diluted Ising systems
de Figueiredo Neto, João Monteiro; de Oliveira, Suzana Maria Moss; de Oliveira, Paulo Murilo Castro
1994-05-01
The finite size scaling renormalisation group (FSSRG) was introduced in Europhysics Letters 20 (1992) 621. Based only on the finite size scaling hypothesis, with no further assumptions, it differs from other real space renormalisation groups (RSRGs) in the following essential point: one does not need to adopt any particular recipe exp(- H‧( S‧/ T = σ sP( S, S‧) exp[- H( S)/ T] relating the spin states S of the original system to the spin states S' of a renormalised system. The choice of a particular weight function P( S, S‧), e.g. the so called majority rule, is generally based on plausibility arguments, and involves uncontrollable approximations. In addition to being free from these drawbacks, FSSRG shares with RSRG some good features as, for instance, the possibility of extracting qualitative informations from multi-parameter RG flow diagrams, including crossovers, universality classes, universality breakings, multicriticalities, orders of transitions, etc. Other unpleasant consequences of particular weight functions, as the so called proliferation of parameters, are also absent in the FSSRG. Using it in three-dimensions, we were able to find a semi-unstable fixed point in the critical frontier concentration p versus exchange coupling J, characterizing a universality class crossover when one goes from pure to diluted Ising ferromagnets. The specific heat exponents we have obtained for the pure and diluted regimes are in agreement with the Harris criterion.
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.
Late-time Domain Growth in the Compressible Triangular Ising Net
Meng, Meng; Landau, David
2012-02-01
We perform large scale Monte Carlo simulations of the long-tme domain growth behavior in a compressible, triangular Ising net. Unlike previous work,ootnotetextMitchell and DP Landau, PRL 97, 025701 (2006) our model has no bond angle interactions or lattice mismatch. The system is quenched below the critical temperature from a homogenous disordered state to an ordered phase where multiple domains coexist. We include an elastic energy part in the Hamiltonian to adjust the rigidity of the model. Theory expects the domain size R(t) grows as a power law R(t)=A+Bt^n, where t is the time after the quench. For the rigid model we find the late-time domain size growth factor n has Lifshitz-Slozov value of 13. For weak flexible models, we get slight reduction from 13. For the strongly flexible model, we get a bimodal distribution of bond lengths and a dramatically reduced value of n, which has similar behavior as the mismatch model.ootnotetextIbid.
Milchev, Andrey; Müller, M.; Binder, K.; Landau, D. P.
2003-09-01
Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic L×L×Ly Ising lattices with nearest neighbor ferromagnetic exchange and four free L×Ly surfaces, at which antisymmetric surface fields ±Hs act, are studied for a wide range of linear dimensions (4⩽L⩽320, 30⩽Ly⩽1000), in an attempt to clarify finite size effects on the wedge filling transition in this “double-wedge” geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature Tc this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,Ly→∞ and T larger than the filling transition temperature Tf(Hs), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For Tinterface is bound either to the wedge where the two surfaces with field -Hs meet (then the total magnetization m of the system is positive) or to the opposite wedge (then minterface midpoint from the wedges is studied as T→Tf(Hs) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l0 for T>Tf(Hs) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length ξy in the y direction along the wedges is also studied, and we find no transition for finite L and Ly→∞. For L→∞ the prediction l0∝(Hsc-Hs)-1/4 is verified, where Hsc(T) is the inverse function of Tf(Hs) and ξy∝(Hsc-Hs)-3/4, respectively. We
Milchev, Andrey; Müller, M; Binder, K; Landau, D P
2003-09-01
Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For Tinterface is bound either to the wedge where the two surfaces with field -H(s) meet (then the total magnetization m of the system is positive) or to the opposite wedge (then minterface midpoint from the wedges is studied as T-->T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the
Replica exchange Monte Carlo simulations of the ising spin glass: Static and dynamic properties
Yucesoy, Burcu
Spin glasses have been the subject of intense study and considerable controversy for decades, and the low-temperature phase of short-range spin glasses is still poorly understood. Our main goal is to improve our understanding in this area and find an answer to the following question: Are there only a single pair or a countable infinity of pure states in the low temperature phase of the EA spin glass? To that aim we first start by introducing spin glasses and provide a brief history of their research, then proceed to describe our method of simulation, the parallel tempering Monte Carlo algorithm. Next, we present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. In order to understand how the parallel tempering algorithm works, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. We examine the correlation between static and dynamic observables for ˜ 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature, and our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape. In the following chapters, the three- and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied again via large scale Monte Carlo simulations at low temperatures, deep within the spin glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. We arrive to the following conclusion: The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a
Kim, Ki-Seok
2016-01-01
We develop a gravity reformulation for a topological phase transition of the Kitaev superconductor model in one dimension. Applying the Wilson's renormalization group procedure repeatedly, we find an effective theory with a renormalized coupling function, where the repetition index of the renormalization group transformation is identified with an extra dimension. Solving the renormalization group equation, we obtain an effective interaction vertex as a function of the extra dimension. The topological quantum phase transition is encoded into the gravity description as follows: First, the inter-site correlation (hopping and pairing) strength of spinless fermions given by a ferromagnetic coupling constant in the transverse-field Ising model is renormalized to vanish in a topologically trivial p-wave superconducting state, adiabatically connected to a trivial insulating behavior. Second, the inter-site correlation strength does not evolve at a quantum critical point, giving rise to a conformal field theory that d...
Directory of Open Access Journals (Sweden)
I.V. Pylyuk
2013-06-01
Full Text Available The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order parameter (the average spin moment of a three-dimensional uniaxial magnet are obtained in approximations of quartic and sextic non-Gaussian fluctuation distributions (the ρ4 and ρ6 models, respectively, taking into account confluent corrections. Some distinctive features appearing in the process of calculating the order parameter on the basis of two successive non-Gaussian approximations are indicated. The dependence of the average spin moment of an Ising-like system on the temperature and microscopic parameters is studied.
Wang, Wei; Chen, Dong-dong; Lv, Dan; Liu, Jin-ping; Li, Qi; Peng, Zhou
2017-09-01
The Monte Carlo method has been used to study the magnetic and thermodynamic properties of a hexagonal ferrimagnetic Ising nanoparticle with spin-3/2 inner core surrounded by spin-1 surface shell layers. The effects of exchange couplings and crystal-fields on the compensation behaviors and critical phenomena of the system have been investigated in detail. Many types of the magnetization curves have been found, depending on the competitions among the exchange couplings, the crystal-fields and the temperature. The phase diagrams for different exchange couplings and crystal-fields have been also obtained. In Particular, we have discovered the double and triple hysteresis loops for certain physical parameters in the present system. An excellent agreement has been achieved from the comparison between our results and the previous studies.
Large-scale Ising spin network based on degenerate optical parametric oscillators
Inagaki, Takahiro; Hamerly, Ryan; Inoue, Kyo; Yamamoto, Yoshihisa; Takesue, Hiroki
2016-01-01
Simulating a network of Ising spins with physical systems is now emerging as a promising approach for solving mathematically intractable problems. Here we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPO), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generated >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing (FWM) in a highly nonlinear fibre (HNLF) placed in a fibre cavity. Using those DOPOs, a one-dimensional (1D) Ising model was simulated by introducing nearest-neighbour optical coupling. We observed the formation of spin domains and found that the domain size diverged near the DOPO threshold, which suggests that the DOPO network can simulate the behavior of low-temperature Ising spins.
Kuum IT-trend 2007 - see oled sina ise! / Andrus Hiiepuu, Ants Sild
Hiiepuu, Andrus, 1966-
2007-01-01
Ajakiri Time kuulutas aasta inimeseks tavalise arvutikasutaja, autorid arutlevad, mida see sina ise IT-vallas võiks tähendada. Infotainment - infotehnoloogia -ja kommunikatsioonivahendite ning meelelahutuse sulandumine
The boundary states and correlation functions of the tricritical Ising model
Balaska, S
2006-01-01
We consider the minimal model describing the tricritical Ising model on the upper half plane or equivalently on an infinite strip of finite width and we determine its consistents boundary states as well as its 1-point correlation functions.
Kuum IT-trend 2007 - see oled sina ise! / Andrus Hiiepuu, Ants Sild
Hiiepuu, Andrus, 1966-
2007-01-01
Ajakiri Time kuulutas aasta inimeseks tavalise arvutikasutaja, autorid arutlevad, mida see sina ise IT-vallas võiks tähendada. Infotainment - infotehnoloogia -ja kommunikatsioonivahendite ning meelelahutuse sulandumine
Numerically exact correlations and sampling in the two-dimensional Ising spin glass.
Thomas, Creighton K; Middleton, A Alan
2013-04-01
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest-neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.
Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14
Paddison, Joseph A. M.; Ong, Harapan S.; Hamp, James O.; Mukherjee, Paromita; Bai, Xiaojian; Tucker, Matthew G.; Butch, Nicholas P.; Castelnovo, Claudio; Mourigal, Martin; Dutton, S. E.
2016-12-01
The Ising model--in which degrees of freedom (spins) are binary valued (up/down)--is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ~0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
Institute of Scientific and Technical Information of China (English)
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
Completeness of the classical 2D Ising model and universal quantum computation.
Van den Nest, M; Dür, W; Briegel, H J
2008-03-21
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.
Surface amorphization in a transverse Ising nanowire; effects of a transverse field
Energy Technology Data Exchange (ETDEWEB)
Kaneyoshi, T., E-mail: kaneyosi@is.nagoya-u.ac.Jp
2017-05-15
Using the effective-field theory with correlations, the phase diagrams and the thermal variations of total magnetization in an Ising nanowire with surface amorphization are investigated by applying a magnetic field to the direction perpendicular to the spin direction. Some unconventional and novel phenomena have been found in them. Furthermore, phase diagrams in the two transverse Ising nanowires with surface amorphizations are compared and discussed.
Inhomogeneous and Self-Organized Temperature in Schelling-Ising Model
Müller, Katharina; Schulze, Christian; Stauffer, Dietrich
The Schelling model of 1971 is a complicated version of a square-lattice Ising model at zero temperature, to explain urban segregation, based on the neighbor preferences of the residents, without external reasons. Various versions between Ising and Schelling models give about the same results. Inhomogeneous "temperatures" T do not change the results much, while a feedback between segregation and T leads to a self-organization of an average T.
Properties of 1D classical and quantum Ising quasicrystals: rigorous results
Yessen, W. N.
2012-01-01
In this paper we consider one-dimensional classical and quantum spin-1=2 quasiperiodic Ising chains, with two-valued nearest neighbor interaction modulated by a Fibonacci substitution sequence on two letters. In the quantum case, we investigate the energy spectrum of the Ising Hamiltonian, in presence of constant transverse magnetic field, by employing the techniques that were developed in our previous work. In the classical case, we investigate and prove analyticity of the free energy functi...
Direct Monte Carlo Measurement of the Surface Tension in Ising Models
Hasenbusch, M
1992-01-01
I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model.
Institute of Scientific and Technical Information of China (English)
赵新军
2012-01-01
In this paper, we use computers to investigate Two-Dimension trangular Ising lattice by means of the Monte Carlo method, and calculated the magnetization and specific heat of Two-Dimensional triangular Ising lattice model in the absence of a magnetic field. We can get the critical temperature by means of the Monte Carlo method. The critical temperature that we obtained by Monte Carlo method is confirmed with the theoretical result very well.%应用MonteCarlo方法计算了无外磁场时二维三角晶格Ising模型的磁化强度、比热随温度的变化关系，给出了二维三角晶格Ising模型的临界温度J/kBT=0．44，由MonteCarlo方法所确定的“临界温度”与理论计算结果一致．
Xiong, Guo-Ming
1991-02-01
By introducing a defect zone instead of a single defect line in the bulk, a modified form of the AB model of Forgacs, Svrakic, and Privman is investigated. It is found that when the defect zone is far away from the substrate the first-order unbinding transition still exists at a temperature T1 below the critical point of the two-dimensional Ising model, while when it is near the substrate no wetting transition can take place because the inhomogeneity constrains the formation of the wetting layer.
Statistical mechanics of the inverse Ising problem and the optimal objective function
Berg, Johannes
2017-08-01
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen, driven by the advent of large-scale data across different scientific disciplines. Recently, strategies to solve the inverse Ising problem based on convex optimisation have proven to be very successful. These approaches maximise particular objective functions with respect to the model parameters. Examples are the pseudolikelihood method and interaction screening. In this paper, we establish a link between approaches to the inverse Ising problem based on convex optimisation and the statistical physics of disordered systems. We characterise the performance of an arbitrary objective function and calculate the objective function which optimally reconstructs the model parameters. We evaluate the optimal objective function within a replica-symmetric ansatz and compare the results of the optimal objective function with other reconstruction methods. Apart from giving a theoretical underpinning to solving the inverse Ising problem by convex optimisation, the optimal objective function outperforms state-of-the-art methods, albeit by a small margin.
Shim, Yong; Jaiswal, Akhilesh; Roy, Kaushik
2017-05-01
Ising spin model is considered as an efficient computing method to solve combinatorial optimization problems based on its natural tendency of convergence towards low energy state. The underlying basic functions facilitating the Ising model can be categorized into two parts, "Annealing and Majority vote." In this paper, we propose an Ising cell based on Spin Hall Effect (SHE) induced magnetization switching in a Magnetic Tunnel Junction (MTJ). The stochasticity of our proposed Ising cell based on SHE induced MTJ switching can implement the natural annealing process by preventing the system from being stuck in solutions with local minima. Further, by controlling the current through the Heavy-Metal (HM) underlying the MTJ, we can mimic the majority vote function which determines the next state of the individual spins. By solving coupled Landau-Lifshitz-Gilbert equations, we demonstrate that our Ising cell can be replicated to map certain combinatorial problems. We present results for two representative problems—Maximum-cut and Graph coloring—to illustrate the feasibility of the proposed device-circuit configuration in solving combinatorial problems. Our proposed solution using a HM based MTJ device can be exploited to implement compact, fast, and energy efficient Ising spin model.
A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems
Takata, Kenta; Marandi, Alireza; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa
2016-09-01
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.
SANS studies of critical phenomena in ternary mixtures
Bulavyn, L A; Hohryakov, A; Garamus, V; Avdeev, M; Almasy, L
2002-01-01
Critical behaviour of a quasi-binary liquid mixture is investigated by small-angle neutron scattering. Analysis of the changes of the critical parameters, caused by addition of a small amount of electrolyte into the binary mixture 3-methylpyridine-heavy water, shows that the third component does not change the 3D Ising-type behaviour of the system; a crossover towards the mean-field behaviour is not observed. (orig.)
Spin-lattice relaxation within a dimerized Ising chain in a magnetic field
Erdem, Rıza; Gülpınar, Gül; Yalçın, Orhan; Pawlak, Andrzej
2014-07-01
A qualitative study of the spin-lattice relaxation within a dimerized Ising chain in a magnetic field is presented. We have first determined the time dependence of the deviation of the lattice distortion parameter δ Δ from the equilibrium state within framework of a technique combining the statistical equilibrium theory based on the transfer matrix method and the linear theory of irreversible thermodynamics. We have shown that the time dependence of the lattice distortion parameter is characterized by a single time constant ( τ) which diverges around the critical point in both dimerized ( Δ ≠ 0) and uniform ( Δ = 0) phase regions. When the temperature and magnetic field are fixed to certain values, the time τ depends only on exchange coupling between the spins. It is a characteristic time associated with the long wavelength fluctuations of distortion. We have also taken into account the effects of spatial fluctuations on the relaxation time using the full Landau-Ginzburg free energy functional. We have found an explicit expression for the relaxation time as a function of temperature, coupling constant and wave vector ( q) and shown that the critical mode corresponds to the case q = 0. Finally, our results are found to be in good qualitative agreement with the results obtained in recent experimental study on synchrotron x-ray scattering and muon spin relaxation in diluted material C u 1- y M g y G e O 3 where the composition y is very close to 0.0209. These results can be considered as natural extensions of some previous works on static aspects of the problem.
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.
Sampaio Filho, C I N; Dos Santos, T B; Moreira, A A; Moreira, F G B; Andrade, J S
2016-05-01
We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability P_{ij}∼r^{-α}, where r_{ij} is the Manhattan distance between nodes i and j, and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000)NATUAS0028-083610.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α≤3 the critical behavior is described by mean-field exponents, while for α≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3<α<4, the critical exponents are dependent on α.
Critical behavior of Y2NiMnO6 double perovskite
Nhalil, Hariharan; Nair, Harikrishnan S.; Elizabeth, Suja
2016-05-01
Critical behavior of double perovskite Y2NiMnO6 near the second-order ferromagnetic transition is studied. Scaling exponents calculated frommodified Arrot plots are confirmed by Kouvel-Fisher method and satisfy the Widom's scaling relation. The exponents do not follow any conventional theoretical models.β values areconsistent with 3D-Ising model whileδconformsto TCMF and γ valueclosely relates to the 3D-Heisenberg model. Critical exponents are compared with similar R2NiMnO6 double perovskites which shows that a decrease in size of R ion changes exponents from mean-field to the 3D-Ising model.
Plasma electrons as tracers of distant magnetotail structure: ISEE-3
Energy Technology Data Exchange (ETDEWEB)
Baker, D.N.; Bame, S.J.; Gosling, J.T.; Gussenhoven, M.S.
1988-01-01
Electrons in the 50-500 eV energy range commonly exhibit strong, field-aligned bidirectional anisotropies in the distant (r > 100 Rg) geomagnetic tail lobes and are found to occur predominantly in the lobe directly connected to the sun along the interplanetary magnetic field in the open magnetosphere model (north lobe for away interplanetary sectors and south lobe for toward sectors). Data show the transition from unidirectional (sheath) electron populations to bidirectional (lobe) populations at the distant magnetopause. This demonstrates the open nature of the distant magnetotail and shows that the source of the higher-energy, bidirectional lobe electrons is the tailward-directed electron heat flux population in the magnetosheath. The field-aligned lobe electron phase space densities above 200 eV at ISEE-3 agree well with DMSP-measured polar rain phase space densities near the polar cap and the spectral slopes above 200 eV also are similar. Below 100-200 eV there is a thermal electron population in the distant tail, arising from local entry of plasma through the distant magnetopause, which is not present at DMSP altitudes. These data show that the suprathermal tail lobe electrons are essentially a test particle population which can move freely along field lines to form polar rain; in contrast, the thermal electrons are bound to the tailward-flowing lobe ion population far down the tail and thus cannot reach the polar cap regions.
On the structure of the distant magnetotail - ISEE 3
Fairfield, D. H.
1992-01-01
The relative frequency of observation of the magnetosheath and magnetotail in the region where a nominal magnetotail is expected is determined on the basis of ISEE-3 magnetic field and electron plasma data. These observations are compared with how frequently a tail of a given radius would be expected to be seen, assuming typical variations in the direction of the solar wind flow relative to the radial. Observations match expectations if the average radius consistent with an open magnetotail where field lines are lost both through the magnetopause and also by closing along the equatorial current sheet. This relatively small radius is consistent with an open magnetotail where field lines are lost both through the magnetopause and also by closing across the equatorial current sheet. The average solar magnetospheric Bz component of the field in the distant plasma sheet is 0.6 nT during quiet times but zero during disturbed times, which suggests that when the polar cap becomes smaller during quiet times, many of the field lines that previously formed the distant tail lobes are converted into closed field lines that cross the equatorial plane earthward of 240 RE.