Mean field models for spin glasses
Talagrand, Michel
2011-01-01
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.
Spectral Gap Estimates in Mean Field Spin Glasses
Ben Arous, Gérard; Jagannath, Aukosh
2018-05-01
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the spectral gap is exponentially small, and thus that mixing is exponentially slow. We then exhibit sufficient conditions on the equilibrium Gibbs measure which guarantee the existence of these barriers, using the notion of replicon eigenvalue and 2D Guerra Talagrand bounds. We show how these sufficient conditions cover large classes of Ising spin models for reversible nearest-neighbor dynamics and spherical models for Langevin dynamics. Finally, in the case of Ising spins, Panchenko's recent rigorous calculation (Panchenko in Ann Probab 46(2):865-896, 2018) of the free energy for a system of "two real replica" enables us to prove a quenched LDP for the overlap distribution, which gives us a wider criterion for slow mixing directly related to the Franz-Parisi-Virasoro approach (Franz et al. in J Phys I 2(10):1869-1880, 1992; Kurchan et al. J Phys I 3(8):1819-1838, 1993). This condition holds in a wider range of temperatures.
Mean-field theory of spin-glasses with finite coordination number
Kanter, I.; Sompolinsky, H.
1987-01-01
The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
Real-Space Application of the Mean-Field Description of Spin-Glass Dynamics
International Nuclear Information System (INIS)
Barrat, Alain; Berthier, Ludovic
2001-01-01
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard 'mean-field theory' versus 'droplet picture' debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed
Magnetic cluster mean-field description of spin glasses in amorphous La-Gd-Au alloys
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Poon, S.J.; Durand, J.
1978-03-01
Bulk magnetic properties of splat-cooled amorphous alloys of composition La/sub 80-x/Gd/sub x/Au 20 (0 less than or equal to x less than or equal to 80) were studied. Zero-field susceptibility, high-field magnetization (up to 75 kOe) and saturated remanence were measured between 1.8 and 290 0 K. Data were analyzed using a cluster mean-field approximation for the spin-glass and mictomagnetic alloys (x less than or equal to 56). Mean-field theories can account for the experimental freezing-temperatures of dilute spin-glasses in which the Ruderman-Kittel-Kasuya-Yosida interaction is dominant. For the dilute alloys, the role of amorphousness on the magnetic interactions is discussed. By extending the mean-field approximation, the concentrated spin-glasses are represented by rigid ferromagnetic clusters as individual spin-entities interacting via random forces. Scaling laws for the magnetization M and saturation remanent magnetization M/sub rs/ are obtained and presented graphically for the x less than or equal to 32 alloys in which M/x = g(H/x*, T/x), M/sub rs/(T)/x = M/sub rs/(0)/x/ exp (-α*T/x/sup p/) where x* is the concentration of clusters, α* is a constant, and p is the freezing-temperature exponent given by T/sub M/ infinity x/sup p/. It is found that p = 1 and 1.3 for the regions 4 less than or equal to x less than or equal to 40 respectively. An attempt is also made to account for the freezing temperatures of concentrated spin glasses. The strength of the interaction among clusters is determined from high-field magnetization measurements using the Larkin-Smith method modified for clusters. It is shown that for the x < 24 alloys, the size of the clusters can be correlated to the structural short-range order in the amorphous state. More concentrated alloys are marked by the emergence of cluster percolation
Simulations of ground state fluctuations in mean-field Ising spin glasses
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Boettcher, Stefan
2010-01-01
The scaling of fluctuations in the distribution of ground state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the extremal optimization heuristic across a range of different models on sparse and dense graphs. These models exhibit very diverse behaviors, and an asymptotic extrapolation is often complicated by higher-order corrections in size. The clearest picture, in fact, emerges from the study of graph bipartitioning, a combinatorial optimization problem closely related to spin glasses. Asides from two-spin interactions with discrete bonds, we also consider problems with Gaussian bonds and three-spin interactions, which behave quite differently
Self-averaging correlation functions in the mean field theory of spin glasses
International Nuclear Information System (INIS)
Mezard, M.; Parisi, G.
1984-01-01
In the infinite range spin glass model, we consider the staggered spin σsub(lambda)associated with a given eigenvector of the interaction matrix. We show that the thermal average of sub(lambda)sup(2) is a self-averaging quantity and we compute it
Critical behavior of mean-field spin glasses on a dilute random graph
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De Sanctis, Luca [Dipartimento di Matematica e di Psicologia, Universita di Bologna, P.zza di Porta San Donato 5, 40126 Bologna (Italy); Barra, Adriano; Folli, Viola [Dipartimento di Fisica, Universita La Sapienza, P.le Aldo Moro 5, 00185 Roma (Italy)], E-mail: desanctis@dm.unibo.it, E-mail: adriano.barra@roma1.infn.it, E-mail: viola.folli@roma1.infn.it
2008-05-30
We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e.g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof.
Critical behavior of mean-field spin glasses on a dilute random graph
International Nuclear Information System (INIS)
De Sanctis, Luca; Barra, Adriano; Folli, Viola
2008-01-01
We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e.g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof
Bovier, Anton
2007-01-01
Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science. This collection of state-of-the-art review papers written by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the mean-field theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models. The book will serve as a concise introduction to the state of the art of spin glass theory, usefull to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Broken symmetry in the mean field theory of the ising spin glass: replica way and no replica way
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De Dominicis, C.
1983-06-01
We review the type of symmetry breaking involved in the solution discovered by Parisi and in the static derivation of the solution first introduced via dynamics by Sompolinsky. We turn to a formulation of the problem due to Thouless, Anderson and Palmer (TAP) that put a set of equations for the magnetization. A probability law for the magnetization is then built. We consider two cases: (i) a canonical distribution which is shown to give indentical results to the Hamiltonian formulation under a weak and physical assumption and (ii) a white distribution characterized by two matrices and a response. We show what symmetry breaking is necessary to recover Sompolinsky free energy. In section III we supplement replica indices in the Hamiltonian approach by ''time'' indices ans show in particular that the analytic continuation involved in Sompolinsky's equilibrium derivation, is trying to mimick a translational symmetry breaking in ''time'' that incorporates Sompolinsky's ansatz of a long time scale sequence. In section IV we apply the same treatment to the white average approach and show that, replicas can be altogether discorded and replaced by ''time''. Finally, we briefly discuss the attribution of distinct answers for the standard spin glass order parameter depending on the physical situation: equilibrium or non equilibrium associated with canonical or white (non canonical) initial conditions and density matrices
Spin and orbital exchange interactions from Dynamical Mean Field Theory
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Secchi, A., E-mail: a.secchi@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands); Lichtenstein, A.I., E-mail: alichten@physnet.uni-hamburg.de [Universitat Hamburg, Institut für Theoretische Physik, Jungiusstraße 9, D-20355 Hamburg (Germany); Katsnelson, M.I., E-mail: m.katsnelson@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands)
2016-02-15
We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii–Moriya interaction and other symmetric terms such as dipole–dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms. - Highlights: • We give formulas for the exchange interaction tensor in strongly correlated systems. • Interactions are written in terms of electronic Green's functions and self-energies. • The method is suitable for a Dynamical Mean Field Theory implementation. • No quenching of the orbital magnetic moments is assumed. • Spin and orbital contributions to magnetism can be computed separately.
Contucci, Pierluigi
2013-01-01
Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.
International Nuclear Information System (INIS)
Mookerjee, Abhijit
1976-01-01
''Spin glasses'', are entire class of magnetic alloys of moderate dilution, in which the magnetic atoms are far enough apart to be unlike the pure metal, but close enough so that the indirect exchange energy between them (mediated by the s-d interaction between local moments and conduction electrons) dominates all other energies. Characteristic critical phenomena displayed such as freezing of spin orientation at 'Tsub(c)' and spreading of magnetic ordering, are pointed out. Anomalous behaviour, associated with these critical phenomena, as reflected in : (i) Moessbauer spectroscopy giving hyperfine splitting at Tsub(c), (ii) maxima in susceptibility and remanent magnetism, (iii) thermopower maxima and change in slope, (iv) Characteristic cusp in susceptibility and its removal by very small magnetic fields, and (v) conductivity-resistivity measurements, are discussed. Theoretical developments aimed at explaining these phenomena, in particular, the ideas from percolation and localisation theories, and the approach based on the gellations of polymers, are discussed. Finally, a new approach based on renormalisation group in disordered systems is also briefly mentioned. (K.B.)
Mean fields and self consistent normal ordering of lattice spin and gauge field theories
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Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
Spin glasses and neural networks
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Parga, N.; Universidad Nacional de Cuyo, San Carlos de Bariloche
1989-01-01
The mean-field theory of spin glass models has been used as a prototype of systems with frustration and disorder. One of the most interesting related systems are models of associative memories. In these lectures we review the main concepts developed to solve the Sherrington-Kirkpatrick model and its application to neural networks. (orig.)
Equilibrium state of the mean-field Potts glass
Czech Academy of Sciences Publication Activity Database
Janiš, Václav; Klíč, Antonín
2011-01-01
Roč. 23, č. 2 (2011), s. 1-5 ISSN 0953-8984 Institutional research plan: CEZ:AV0Z10100520 Keywords : Potts glass * replica-symmetry breaking * asymptotic expansion Subject RIV: BE - Theoretical Physics Impact factor: 2.546, year: 2011 http://iopscience.iop.org/0953-8984/23/2/022204/
Virtual-site correlation mean field approach to criticality in spin systems
International Nuclear Information System (INIS)
Sen, Aditi; Sen, Ujjwal
2013-01-01
We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories
An RVB state with fermionic charges and bosonic spins: Mean field theory
International Nuclear Information System (INIS)
Flensberg, K.; Hedegard, P.; Brix Pedersen, M.
1989-01-01
We consider a representation of the Hubbard model, in which the charge carriers are fermions and the spin carriers are bosons. We show that there exist a mean-field solution with a condensate of spin-singlets and we characterize the low temperature behavior of the quasiparticles. Finally we calculate the tunneling spectrum for a normal metal-RVB state tunnel junction and suggest the tunneling experiment as a probe of the statistics of the RVB quasiparticles. (orig.)
Realization of the mean-field universality class in spin-crossover materials
Miyashita, Seiji; Konishi, Yusuké; Nishino, Masamichi; Tokoro, Hiroko; Rikvold, Per Arne
2008-01-01
In spin-crossover materials, the volume of a molecule changes depending on whether it is in the high-spin (HS) or low-spin (LS) state. This change causes distortion of the lattice. Elastic interactions among these distortions play an important role for the cooperative properties of spin-transition phenomena. We find that the critical behavior caused by this elastic interaction belongs to the mean-field universality class, in which the critical exponents for the spontaneous magnetization and the susceptibility are β=1/2 and γ=1 , respectively. Furthermore, the spin-spin correlation function is a constant at long distances, and it does not show an exponential decay in contrast to short-range models. The value of the correlation function at long distances shows different size dependences: O(1/N) , O(1/N) , and constant for temperatures above, at, and below the critical temperature, respectively. The model does not exhibit clusters, even near the critical point. We also found that cluster growth is suppressed in the present model and that there is no critical opalescence in the coexistence region. During the relaxation process from a metastable state at the end of a hysteresis loop, nucleation phenomena are not observed, and spatially uniform configurations are maintained during the change of the fraction of HS and LS. These characteristics of the mean-field model are expected to be found not only in spin-crossover materials, but also generally in systems where elastic distortion mediates the interaction among local states.
Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi
2016-10-07
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
Muon spin relaxation measurements of spin-correlation decay in spin-glass AgMn
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Heffner, R.H.; Cooke, D.W.; Leon, M.; Schillaci, M.E. (Los Alamos National Lab., NM (USA)); MacLaughlin, D.E.; Gupta, L.C. (California Univ., Riverside (USA))
1984-01-01
The field (H) dependence of the muon longitudinal spin-lattice relaxation rate well below the spin glass temperature in AgMn is found to obey an algebraic form given by (H)sup(..gamma..-1), with ..gamma.. = 0.54 +- 0.05. This suggests that Mn spin correlations decay with time as tsup(-..gamma..), in agreement with mean field theories of spin-glass dynamics which yield ..gamma..
Muon spin relaxation measurements of spin-correlation decay in spin-glass AgMn
International Nuclear Information System (INIS)
Heffner, R.H.; Cooke, D.W.; Leon, M.; Schillaci, M.E.; MacLaughlin, D.E.; Gupta, L.C.
1984-01-01
The field (H) dependence of the muon longitudinal spin-lattice relaxation rate well below the spin glass temperature in AgMn is found to obey an algebraic form given by (H)sup(γ-1), with γ = 0.54 +- 0.05. This suggests that Mn spin correlations decay with time as tsup(-γ), in agreement with mean field theories of spin-glass dynamics which yield γ < approx. 0.5. Near the glass temperature the agreement between the data and theory is not as good. (Auth.)
Mean-field solution of the Potts glass near the transition temperature to the ordered phase
Czech Academy of Sciences Publication Activity Database
Janiš, Václav; Klíč, Antonín
2011-01-01
Roč. 84, č. 6 (2011), "064446-1"-"064446-10" ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100520 Keywords : Potts glass * hierarchic solutions with replicated spins * continuous replica-symmetry breaking Subject RIV: BE - Theoretical Physics Impact factor: 3.691, year: 2011
The spin glasses: the paradigm of the complex systems
International Nuclear Information System (INIS)
Ruiz-Lorenzo, J.J.
1997-01-01
The solution of the spin glasses in the Mean Field approximation gives some interesting characteristics such as the existence of an infinite number of pure states organized in an ultrametric way (like in Taxonomy). These properties raise the spin glasses to a paradigm of the complex systems. (Author) 7 refs
A dynamic mean-field glass model with reversible mode coupling and a trivial Hamiltonian
International Nuclear Information System (INIS)
Kawasaki, Kyozi; Kim, Bongsoo
2002-01-01
Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise account of our toy model developed to gain more insight into MCT. We then reduce this toy model by adiabatically eliminating rapidly varying velocity-like variables to obtain a Fokker-Planck equation for the slowly varying density-like variables where the diffusion matrix can be singular. This gives room for non-ergodic stationary solutions of the above equation. (author)
Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems
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Jiasen Jin
2016-07-01
Full Text Available We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1/2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.
Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids
Szamel, Grzegorz
2017-10-01
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016), 10.1103/PhysRevLett.116.015902]. Our approach provides an alternative, physically motivated derivation of this result.
An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model
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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.
Superconductive analogue of spin glasses
International Nuclear Information System (INIS)
Feigel'man, M.; Ioffe, L.; Vinokur, V.; Larkin, A.
1987-07-01
The properties of granular superconductors in magnetic fields, namely the existence of a new superconductive state analogue of the low-temperature superconductive state in spin glasses are discussed in the frame of the infinite-range model and the finite-range models. Experiments for elucidation of spin-glass superconductive state in real systems are suggested. 30 refs
Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms
Kulske, Christof; Opoku, Alex A.
2008-01-01
We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous
Muon spin-relaxation measurements of spin-correlation decay in spin-glass AgMn
International Nuclear Information System (INIS)
Heffner, R.H.; Cooke, D.W.; Leon, M.; Schillaci, M.E.; MacLaughlin, D.E.; Gupta, L.C.
1983-01-01
The field (H) dependence of the muon longitudinal spin-lattice relaxation rate well below the spin-glass temperature in AgMn is found to obey an algebraic form given by (H)/sup nu-1/, with nu = 0.54 +- 0.05. This suggests that Mn spin correlations decay with time as t - /sup nu/, in agreement with mean field theories of spin-glass dynamics which yield nu less than or equal to 0.5. Near the glass temperature the agreement between the data and theory is not as good
International Nuclear Information System (INIS)
Wrobel, P.; Jacak, L.
1988-01-01
It is shown theoretically that the superconducting transition in the framework of RVB mean field treatment in nearly half-filled band Hubbard model is substantially influenced by spin density wave instability. The reasonable SDW and SC ordering phase diagram for doped La 2 CuO 4 compounds is found
Some recent developments in spin glasses
Indian Academy of Sciences (India)
I give some experimental and theoretical background to spin glasses, and then discuss the nature of the phase transition in spin glasses with vector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite-size scaling analysis of the correlation length of the ...
Wieser, R
2017-05-04
A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.
Numerical detection of the Gardner transition in a mean-field glass former.
Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Rainone, Corrado; Seoane, Beatriz; Zamponi, Francesco
2015-07-01
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.
Some recent developments in spin glasses
Indian Academy of Sciences (India)
I give some experimental and theoretical background to spin glasses, and then discuss the ... Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. ..... with equal probability. This has a ...
Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems
International Nuclear Information System (INIS)
Sandvik, A.W.
1999-01-01
A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society
Percolation and spin glass transition
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Sadiq, A.; Tahir-Kheli, R.A.; Wortis, M.; Bhatti, N.A.
1980-10-01
The behaviour of clusters of curved and normal plaquette particles in a bond random, +-J, Ising model is studied in finite square and triangular lattices. Computer results for the concentration of antiferromagnetic bonds when percolating clusters first appears are found to be close to those reported for the occurrence and disappearance of spin glass phases in these systems. (author)
Relaxations in spin glasses: Similarities and differences from ordinary glasses
International Nuclear Information System (INIS)
Ngai, K.L.; Rajagopal, A.K.; Huang, C.Y.
1984-01-01
Relaxation phenomena have become a major concern in the physics of spin glasses. There are certain resemblances of these relaxation properties to those of ordinary glasses. In this work, we compare the relaxation properties of spin glasses near the freezing temperature with those of glasses near the glass transition temperature. There are similarities between the two types of glasses. Moreover, the relaxation properties of many glasses and spin glasses are in conformity with two coupled ''universality'' relations predicted by a recent model of relaxations in condensed matter
Spin-glass transition in disordered terbium
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Hauser, J.J.
1985-01-01
While crystalline Tb is a helix antiferromagnet with a Neel temperature of 229 K which becomes ferromagnetic at 222 K, disordered Tb exhibits a spin-glass transition. The spin-glass freezing temperature ranges from 183 to 53 K, the lowest temperatures corresponding to the greatest degree of atomic disorder. These experiments constitute the first evidence for an elemental spin-glass. (author)
Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field
Borelli, M. E. S.; Carneiro, C. E. I.
1996-02-01
We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P( Δi) = pδ( Δi - Δ) + (1 - p) δ( Δi). We analyse the effects of randomness on the first-order surfaces of the Δ- T- H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.
Algebraic topology of spin glasses
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Koma, Tohru
2011-01-01
We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.
Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi
2018-05-01
We investigate a two-orbital Hubbard model on a honeycomb structure, with a special focus on the antisymmetric spin-orbit coupling (ASOC) induced by symmetry breaking in the electronic degrees of freedom. By investigating the ground-state phase diagram by the mean-field approximation in addition to the analysis in the strong correlation limit, we obtain a variety of symmetry-broken phases that induce different types of effective ASOCs by breaking of spatial inversion symmetry. We find several unusual properties emergent from the ASOCs, such as a linear magnetoelectric effect in a spin-orbital ordered phase at 1/4 filling and a spin splitting in the band structure in charge ordered phases at 1/4 and 1/2 fillings. We also show that a staggered potential on the honeycomb structure leads to another type of ASOC, which gives rise to a valley splitting in the band structure at 1/2 filling. We discuss the experimental relevance of our results to candidate materials including transition metal dichalcogenides and trichalcogenides.
International Nuclear Information System (INIS)
Wei Guozhu; Miao Hailing
2009-01-01
The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Transverse Ising spin-glass model
International Nuclear Information System (INIS)
Santos, Raimundo R. dos; Santos, R.M.Z. dos.
1984-01-01
The zero temperature behavior of the Transverse Ising spin-glass (+-J 0 ) model is discussed. The d-dimensional quantum model is shown to be equivalent to a classical (d + 1)- dimensional Ising spin-glass with correlated disorder. An exact Renormalization Group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin-glass in two-dimensions. (Author) [pt
Evidence for power-law spin-correlation decay from muon spin relaxation in AgMn spin-glass
International Nuclear Information System (INIS)
MacLaughlin, D.E.; Gupta, L.C.; Cooke, D.W.; Heffner, R.H.; Leon, M.; Schillaci, M.E.
1983-01-01
Muon spin relaxation measurements have been carried out below the ''glass'' temperature T/sub g/ in AgMn spin-glasses. The muon spin-lattice relaxation rate varies with field H as H/sup -0.46plus-or-minus0.05/ for 0.30< or =T/T/sub g/< or =0.66. This suggests that impurity-spin correlations decay with time as t/sup -nu/, νapprox. =0.54 +- 0.05, in contrast to the more usual exponential decay. The present data therefore agree quantitatively with the prediction νapprox. =(1/2) of mean-field dynamic theories
International Nuclear Information System (INIS)
Krakoviack, V.
2007-01-01
Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the spherical s+p mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that the phase behavior of these systems is not yet fully understood when s and p are well separated. First, there seems to be a possibility of glass-glass transition scenarios in these systems. Second, we find clear indications that the 1RSB solution cannot be correct in the full glassy phase. Therefore, while the proposed analysis is clearly naive and probably inexact, it definitely calls for a reassessment of the physics of these systems, with the promise of potentially interesting developments in the theory of disordered and complex systems
Portfolios with nonlinear constraints and spin glasses
Gábor, Adrienn; Kondor, I.
1999-12-01
In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.
Spherical 2+p spin-glass model: An exactly solvable model for glass to spin-glass transition
International Nuclear Information System (INIS)
Crisanti, A.; Leuzzi, L.
2004-01-01
We present the full phase diagram of the spherical 2+p spin-glass model with p≥4. The main outcome is the presence of a phase with both properties of full replica symmetry breaking phases of discrete models, e.g., the Sherrington-Kirkpatrick model, and those of one replica symmetry breaking. This phase has a finite complexity which leads to different dynamic and static properties. The phase diagram is rich enough to allow the study of different kinds of glass to spin glass and spin glass to spin glass phase transitions
Irreversibility and self-organization in spin glasses. 1. Origin of irreversibility in spin glasses
International Nuclear Information System (INIS)
Kovrov, V.P.; Kurbatov, A.M.
1989-05-01
The origin of irreversibility in spin glasses is found out on the basis of the analytical study of the well-known TAP equations. Connection between irreversible jumpwise transitions and a positive feedback in spin glasses is discussed. (author). 7 refs, 4 figs
Antibacterial properties of laser spinning glass nanofibers.
Echezarreta-López, M M; De Miguel, T; Quintero, F; Pou, J; Landin, M
2014-12-30
A laser-spinning technique has been used to produce amorphous, dense and flexible glass nanofibers of two different compositions with potential utility as reinforcement materials in composites, fillers in bone defects or scaffolds (3D structures) for tissue engineering. Morphological and microstructural analyses have been carried out using SEM-EDX, ATR-FTIR and TEM. Bioactivity studies allow the nanofibers with high proportion in SiO2 (S18/12) to be classified as a bioinert glass and the nanofibers with high proportion of calcium (ICIE16) as a bioactive glass. The cell viability tests (MTT) show high biocompatibility of the laser spinning glass nanofibers. Results from the antibacterial activity study carried out using dynamic conditions revealed that the bioactive glass nanofibers show a dose-dependent bactericidal effect on Sthaphylococcus aureus (S. aureus) while the bioinert glass nanofibers show a bacteriostatic effect also dose-dependent. The antibacterial activity has been related to the release of alkaline ions, the increase of pH of the medium and also the formation of needle-like aggregates of calcium phosphate at the surface of the bioactive glass nanofibers which act as a physical mechanism against bacteria. The antibacterial properties give an additional value to the laser-spinning glass nanofibers for different biomedical applications, such as treating or preventing surgery-associated infections. Copyright © 2014 Elsevier B.V. All rights reserved.
On the use of spin glass concepts in random automata networks
Energy Technology Data Exchange (ETDEWEB)
Miranda, E N; Parga, N
1988-06-01
We apply concepts and techniques developed in the context of the mean-field theory of spin glasses to networks of random automata. This approach, proposed recently by Derrida and Flyvbjerg, may be useful in understanding the multivalley structure of the Kauffman model.
Spin-chirality decoupling in Heisenberg spin glasses and related systems
Kawamura, Hikaru
2006-01-01
Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real spin-glass transition and its experimental consequence on the ordering of Heisenberg-like spin glasses are discussed.
Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
Hukushima, K.; Kawamura, H.
2000-01-01
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance ...
Rational decisions, random matrices and spin glasses
Galluccio, Stefano; Bouchaud, Jean-Philippe; Potters, Marc
We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each of them is fragile: rationality is in this case of limited use. In addition, this problem is related to spin glasses with Lévy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.
International Nuclear Information System (INIS)
Zozoulenko, I V; Ihnatsenka, S
2008-01-01
We have developed a mean-field first-principles approach for studying electronic and transport properties of low dimensional lateral structures in the integer quantum Hall regime. The electron interactions and spin effects are included within the spin density functional theory in the local density approximation where the conductance, the density, the effective potentials and the band structure are calculated on the basis of the Green's function technique. In this paper we present a systematic review of the major results obtained on the energetics, spin polarization, effective g factor, magnetosubband and edge state structure of split-gate and cleaved-edge overgrown quantum wires as well as on the conductance of quantum point contacts (QPCs) and open quantum dots. In particular, we discuss how the spin-resolved subband structure, the current densities, the confining potentials, as well as the spin polarization of the electron and current densities in quantum wires and antidots evolve when an applied magnetic field varies. We also discuss the role of the electron interaction and spin effects in the conductance of open systems focusing our attention on the 0.7 conductance anomaly in the QPCs. Special emphasis is given to the effect of the electron interaction on the conductance oscillations and their statistics in open quantum dots as well as to interpretation of the related experiments on the ultralow temperature saturation of the coherence time in open dots
Interaction-flip identities in spin glasses
Contucci, P.; Giardinà, C.; Giberti, C.
2009-01-01
We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of the flipped region. Using a new interpolation method, which
Random complex automata: Analogy with spin glasses
International Nuclear Information System (INIS)
Flyvbjerg, H.
1986-12-01
Ab initio properties of random networks of automata have been studied statistically. A strikingly high degree of similarity is demonstrated between the multivalley structure of the basins of attraction of Kauffman's model and that of infinite range spin glasses. Results from simulations as well as exact analytical results are presented. (orig.)
The Order Parameter in a Spin Glass
Enter, A.C.D. van; Griffiths, Robert B.
1983-01-01
Various possible precise definitions of an Edwards-Anderson type of order parameter for an Ising model spin glass are considered, using boundary conditions for a finite system, states of an infinite system, and a duplicate-system approach. Several of these definitions are shown to yield identical
Contrasting the magnetic response between magnetic-glass and reentrant spin-glass
Roy, S. B.; Chattopadhyay, M. K.
2008-01-01
Magnetic-glass is a recently identified phenomenon in various classes of magnetic systems undergoing a first order magnetic phase transition. We shall highlight here a few experimentally determined characteristics of magnetic-glass and the relevant set of experiments, which will enable to distinguish a magnetic-glass unequivocally from the well known phenomena of spin-glass and reentrant spin-glass.
International Nuclear Information System (INIS)
Ertaş, Mehmet; Keskin, Mustafa
2012-01-01
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
Energy Technology Data Exchange (ETDEWEB)
Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2012-07-23
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
Knolle, Johannes; Bhattacharjee, Subhro; Moessner, Roderich
2018-04-01
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the K -J -Γ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material α -RuCl3 in the light of the results from this extended parton theory.
± J D-vector spin glass phase diagram and critical behaviour
International Nuclear Information System (INIS)
Coutinho, S.; Lyra, M.L.
1988-01-01
The phase diagram and the correlation length exponents of the ± J D-Vector Spin-Glass model are studied in the framework of the real space mean field renormalization group method. The boundary between the spin-glass (SG) and the ferromagnetic (F) phases is obtained from the renormalization flow equations and shows a reentrant behaviour over the SG region. This re-entrance increases smoothly with the coordination number. Analytical expressions for the thermal and the correlation length exponents are calculated straight forwardly for all fixed points and figures are presented and compared with availables results from other methods and data. (author) [pt
Heisenberg spin glass experiments and the chiral ordering scenario
International Nuclear Information System (INIS)
Campbell, Ian A.; Petit, Dorothee C.M.C.
2010-01-01
An overview is given of experimental data on Heisenberg spin glass materials so as to make detailed comparisons with numerical results on model Heisenberg spin glasses, with particular reference to the chiral driven ordering transition scenario due to Kawamura and collaborators. On weak anisotropy systems, experiments show critical exponents which are very similar to those estimated numerically for the model Heisenberg chiral ordering transition but which are quite different from those at Ising spin glass transitions. Again on weak anisotropy Heisenberg spin glasses, experimental torque data show well defined in-field transverse ordering transitions up to strong applied fields, in contrast to Ising spin glasses where fields destroy ordering. When samples with stronger anisotropies are studied, critical and in-field behavior tend progressively towards the Ising limit. It can be concluded that the essential physics of laboratory Heisenberg spin glasses mirrors that of model Heisenberg spin glasses, where chiral ordering has been demonstrated numerically. (author)
Simplicity of state and overlap structure in finite-volume realistic spin glasses
International Nuclear Information System (INIS)
Newman, C.M.; Stein, D.L.
1998-01-01
We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of δ functions at ±q EA . This rules out the nonstandard mean-field picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the possibility of even limited versions of mean-field ordering in realistic spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes. copyright 1998 The American Physical Society
Spin Glasses : Statics and Dynamics : Summer School
Bovier, Anton
2009-01-01
Over the last decade, spin glass theory has turned from a fascinating part of t- oretical physics to a ?ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious “Parisi solution” of the Sherrington–Kirkpatrick mean ?eld model of spin glasses, due to the work of Guerra, Talagrand, and others. At the same time, new aspects and applications of the methods developed there have come up. The presentvolumecollects a number of reviewsaswellas shorterarticlesby lecturers at a summer school on spin glasses that was held in July 2007 in Paris. These articles range from pedagogical introductions to state of the art papers, covering the latest developments. In their whole, they give a nice overview on the current state of the ?eld from the mathematical side. The review by Bovier and Kurkova gives a concise introduction to mean ?eld models, starting with the Curie–...
A Kondo cluster-glass model for spin glass Cerium alloys
International Nuclear Information System (INIS)
Zimmer, F M; Magalhaes, S G; Coqblin, B
2011-01-01
There are clear indications that the presence of disorder in Ce alloys, such as Ce(Ni,Cu) or Ce(Pd,Rh), is responsible for the existence of a cluster spin glass state which changes continuously into inhomogeneous ferromagnetism at low temperatures. We present a study of the competition between magnetism and Kondo effect in a cluster-glass model composed by a random inter-cluster interaction term and an intra-cluster one, which contains an intra-site Kondo interaction J k and an inter-site ferromagnetic one J 0 . The random interaction is given by the van Hemmen type of randomness which allows to solve the problem without the use of the replica method. The inter-cluster term is solved within the cluster mean-field theory and the remaining intra-cluster interactions can be treated by exact diagonalization. Results show the behavior of the cluster glass order parameter and the Kondo correlation function for several sizes of the clusters, J k , J 0 and values of the ferromagnetic inter-cluster average interaction I 0 . Particularly, for small J k , the magnetic solution is strongly dependent on I 0 and J 0 and a Kondo cluster-glass or a mixed phase can be obtained, while, for large J k , the Kondo effect is still dominant, both in good agreement with experiment in Ce(Ni,Cu) or Ce(Pd,Rh) alloys.
Thermal conductivity of a superconducting spin-glass
International Nuclear Information System (INIS)
Crisan, M.
1988-01-01
The temperature dependence of the thermal conductivity for a superconducting spin-glass is calculated, taking a short-range spin-spin interaction in a super-conductor carrying a uniform flow. The presence of the short-range interaction between frozen spins gives rise to a strong depression in the thermal conductivity
Koh, Yang Wei
2018-03-01
In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.
Parisi function for two spin glass models
International Nuclear Information System (INIS)
Sibani, P.; Hertz, J.A.
1984-01-01
The probability distribution function P(q) for the overlap of pairs of metastable states and the associated Parisi order function q(x) are calculated exactly at zero temperature for two simple models. The first is a chain in which each spin interacts randomly with the sum of all the spins between it and one end of the chain; the second is an infinite-range limit of a spin glass version of Dyson's hierarchical model. Both have nontrivial overlap distributions: In the first case the problem reduces to a variable-step-length random walk problem, leading to q(x)=sin(πx). In the second model P(q) can be calculated by a simple recursion relation which generates devil's staircase structure in q(x). If the fraction p of antiferromagnetic bonds is less than 1/√2, the staircase is complete and the fractal dimensionality of the complement of the domain where q(x) is flat is log 2/log (1/p 2 ). In both models the space of metastable states can be described in terms of Cayley trees, which however have a different physical interpretation than in the S.K. model. (orig.)
Inverse freezing in the Hopfield fermionic Ising spin glass with a transverse magnetic field
International Nuclear Information System (INIS)
Morais, C.V.; Zimmer, F.M.; Magalhaes, S.G.
2011-01-01
The Hopfield fermionic Ising spin glass (HFISG) model in the presence of a magnetic transverse field Γ is used to study the inverse freezing transition. The mean field solution of this model allows introducing a parameter a that controls the frustration level. Particularly, in the present fermionic formalism, the chemical potential μ and the Γ provide a magnetic dilution and quantum spin flip mechanism, respectively. Within the one step replica symmetry solution and the static approximation, the results show that the reentrant transition between the spin glass and the paramagnetic phases, which is related to the inverse freezing for a certain range of μ, is gradually suppressed when the level of frustration a is decreased. Nevertheless, the quantum fluctuations caused by Γ can destroy this inverse freezing for any value of a.
Critical properties of a simple spin glass model
International Nuclear Information System (INIS)
Aharony, A.; Imry, Y.
1976-01-01
The Mattis spin glass model is described as following from a particular quenched random solid solution picture, and its zero-field properties are discussed. The random field model is reviewed. The application to the spin glass problem is made and the more general scaling theory presented, and the limitations of the model are discussed
Muon spin rotation and other microscopic probes of spin-glass dynamics
International Nuclear Information System (INIS)
MacLaughlin, D.E.
1980-01-01
A number of different microscopic probe techniques have been employed to investigate the onset of the spin-glass state in dilute magnetic alloys. Among these are Moessbauer-effect spectroscopy, neutron scattering, ESR of the impurity spins, host NMR and, most recently, muon spin rotation and depolarization. Spin probes yield information on the microscopic static and dynamic behavior of the impurity spins, and give insight into both the spin freezing process and the nature of low-lying excitations in the ordered state. Microscopic probe experiments in spin glasses are surveyed, and the unique advantages of muon studies are emphasized
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Gomes, Diogo A.
2014-01-01
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Calorimetric investigation of an yttrium-dysprosium spin glass
International Nuclear Information System (INIS)
Wenger, L.E.
1978-01-01
In an effort to compare the spin glass characteristics of yttrium--rare earth alloys with those of the noble-metal spin glasses, the susceptibility and heat capacity of Y/sub 0.98/Dy/sub 0.02/ have been measured in the temperature range 2.5--40 K. The low-field ac susceptibility measurement shows the characteristic cusp-like peak at 7.64 K. The magnetic specific heat of the same sample shows a peak at 7.0 K and may be qualitatively described as a semi-cusp. The magnetic entropy change from absolute zero to 7 K is approximately 0.52 of cR ln(2J+1). These results are qualitatively different than previous calorimetric results on the archetypal spin glasses, AuFe and CuMn, where rounded maxima are observed at temperatures above the spin glass transition temperatures
Stimulated nuclear spin echos and spectral diffusion in glasses
International Nuclear Information System (INIS)
Borges, N.M.; Engelsberg, M.
1984-01-01
Experimental results of stimulated nuclear spin echos decay in glasses are presented. The measurements were performed in B 2 O 3 glasses, at the 23Na and 11 B resonance lines. The data analysis allows the study of Spectral diffusion at an inhomogeneous nuclear magnetic (NMR) resonance line, broadened for a desordered system of nuclear spins. A model is proposed to explain the time constants, and the particular form of the decay. (A.C.A.S.) [pt
Spin glasses and algorithm benchmarks: A one-dimensional view
International Nuclear Information System (INIS)
Katzgraber, H G
2008-01-01
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore large-scale numerical simulations are the tool of choice. Concepts and algorithms derived from the study of spin glasses have been applied to diverse fields in computer science and physics. In this work a one-dimensional long-range spin-glass model with power-law interactions is discussed. The model has the advantage over conventional systems in that by tuning the power-law exponent of the interactions the effective space dimension can be changed thus effectively allowing the study of large high-dimensional spin-glass systems to address questions as diverse as the existence of an Almeida-Thouless line, ultrametricity and chaos in short range spin glasses. Furthermore, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms
Replica analysis of partition-function zeros in spin-glass models
International Nuclear Information System (INIS)
Takahashi, Kazutaka
2011-01-01
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distributions of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.
Mean field approach to nuclear structure
International Nuclear Information System (INIS)
Nazarewicz, W.; Tennessee Univ., Knoxville, TN
1993-01-01
Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd
Development of mean field theories in nuclear physics and in desordered media
International Nuclear Information System (INIS)
Orland, Henri.
1981-04-01
This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr
Production of entropy on simplified dynamics in spin glass systems
Saakyan, D B
2001-01-01
In models of spin glasses one eliminates condition of extreme based on one of the order parameters. On the basis of the available expression for static sum one derived the effective hamiltonian for parameter and the appropriate energy. Relaxation of the system is studied as energy exchange between the degree of freedom related to the order slow parameter and with the rest of the system. At that level one may indicate point of glass capture within phase space on the basis of the static solutions. One studies p-spin model without magnetic field in case of replica symmetry violation. One studies dynamics of p-spin glass in magnetic field in replica-symmetrical phase. One studied model of spins with quadratic interaction when dynamic constants had temperature differing from temperature of space
Magnetic excitations in CuMn spin-glass alloys
International Nuclear Information System (INIS)
Tsunoda, Y.; Kunitomi, N.; Cable, J.W.
1985-01-01
Recent neutron scattering measurements have helped to clarify two important features of CuMn spin glasses. Murani and co-workers have studied the dynamical behavior of spin-glass systems and have observed characteristic ferromagnetic spin correlations with a broad distribution of relaxation times and a dynamical freezing process. By means of the polarization analysis technique, Cable and co-workers have observed the coexistence of two types of magnetic short-range order (MSRO): one is a modulated-spin structure, and the other is a ferromagnetic cluster associated with the atomic short-range order (ASRO). These ordered regions produce diffraction maxima which are found at the (1 1/2 +/- delta 0) and the (1 1/2 0) reciprocal lattice points, respectively. Both of these observations seem to be essential for understanding the CuMn spin-glass system. However, the physical relationship of these properties is not yet understood. The authors have studied the inelastic scattering of neutrons around the magnetic diffuse peak positions of a Cu/sub 78.7/Mn/sub 21.3/ single crystal. The spin-glass freezing temperature of a CuMn alloy with this Mn concentration is estimated to be T/sub f/ approx. 90 K. Most of the data were taken by scanning along the [0 1 0] direction from the (1 0 0) to the (1 1 0) reciprocal lattice points
Effects of finite size on spin glass dynamics
Sato, Tetsuya; Komatsu, Katsuyoshi
2010-12-01
In spite of comprehensive studies to clarify a variety of interesting phenomena of spin glasses, their understanding has been insufficiently established. To overcome such a problem, fabrication of a mesoscopic spin glass system, whose dynamics can be observed over the entire range to the equilibrium, is useful. In this review the challenges of research that has been performed up to now in this direction and our recent related studies are introduced. We have established to study the spin glass behaviour in terms of droplet picture using nanofabricated mesoscopic samples to some extent, but some problems that should be clarified have been left. Finally, the direction of some new studies is proposed to solve the problems.
Spin dynamics in the anisotropic spin glass Fe2TiO5
DEFF Research Database (Denmark)
Yeshurun, Y.; Tholence, J. L.; Kjems, Jørgen
1985-01-01
We have studied spin-freezing phenomena along the magnetic easy axis of the insulating spin glass Fe2TiOS by magnetisation, AC susceptibility and neutron scattering experiments. The characteristic measurement time for these techniques varies over more than fourteen orders of magnitude. The results...
Magnetization relaxation in spin glasses above transition point
International Nuclear Information System (INIS)
Zajtsev, I.A.; Minakov, A.A.; Galonzka, R.R.
1988-01-01
Magnetization relaxation of Cd 0.6 Zn 0.4 Cr 2 Se 4 and Cd 0.6 Mn 0.4 Te monocrystalline samples with T g =21 K and T g =12 K respectively and magnetic colloid is investigated. It is shown that magnetization inexponential relaxation detected experimentally in spin and dipole glasses is essentially higher than T g temperature transition. It is found that at temperatures higher than T g the essential difference is observed in behaviour of spin glasses with different Z and disorder types
Low-field susceptibilities of rare earth spin glass alloys
International Nuclear Information System (INIS)
Sarkissian, B.V.B.
1977-01-01
Static susceptibility in various applied fields and AC susceptibility data on Sc 13% Gd and Sc 4.5% Tb spin glass alloys are reported. The data show that the sharp peak at the freezing temperature, Tsub(g), normally observed in the low-field susceptibility of spin glasses containing 3d magnetic impurities is observed here in the case of Gd, which is an S state solute, but not for Tb. On the contrary, for the Sc-Tb alloy a rather rounded maximum is observed which becomes slightly sharper with increasing applied magnetic fields. (author)
Experimental evidence for dynamic scaling in spin glasses
Pappas, C; Ehlers, G; Campbell, I A
2002-01-01
Dynamics is the key to the understanding of glassy transitions. A detailed analysis of s(Q,t) in the spin glass system Au sub 0 sub . sub 8 sub 6 Fe sub 0 sub . sub 1 sub 4 shows that at T sub g the autocorrelation function decays as t sup - sup x , with x propor to 0.12. Above T sub g , s(Q,t) is then described by the form proposed by Ogielski: t sup - sup x exp(-(t/tau sub 0) supbeta). These results agree with predictions of large scale numerical simulations and are a direct confirmation of dynamic scaling in spin glasses. (orig.)
Interfaces and the Question of Regional Congruence in Spin Glasses
International Nuclear Information System (INIS)
Newman, C. M.; Stein, D. L.
2001-01-01
We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala and Martin and separately by Palassini and Young in spatial dimensions d=3,4. We show that such excitations, with interface dimension d s < d, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any d but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed
Analogy between spin glasses and Yang--Mills fluids
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, B.A.
1988-01-01
A dictionary of correspondence is established between the dynamical variables for spin-glass fluid and Yang-Mills plasma. The Lie-algebraic interpretation of these variables is presented for the two theories. The noncanonical Poisson bracket for the Hamiltonian dynamics of an ideal spin glass is shown to be identical to that for the dynamics of a Yang--Mills fluid plasma, although the Hamiltonians differ for the two theories. This Poisson bracket is associated to the dual space of an infinite-dimensional Lie algebra of semidirect-product type
Spin Glass Models of Syntax and Language Evolution
Siva, Karthik; Tao, Jim; Marcolli, Matilde
2015-01-01
Using the SSWL database of syntactic parameters of world languages, and the MIT Media Lab data on language interactions, we construct a spin glass model of language evolution. We treat binary syntactic parameters as spin states, with languages as vertices of a graph, and assigned interaction energies along the edges. We study a rough model of syntax evolution, under the assumption that a strong interaction energy tends to cause parameters to align, as in the case of ferromagnetic materials. W...
Manganite/Cuprate Superlattice as Artificial Reentrant Spin Glass
Ding, Junfeng
2016-05-04
Emerging physical phenomena at the unit-cell-controlled interfaces of transition-metal oxides have attracted lots of interest because of the rich physics and application opportunities. This work reports a reentrant spin glass behavior with strong magnetic memory effect discovered in oxide heterostructures composed of ultrathin manganite La0.7Sr0.3MnO3 (LSMO) and cuprate La2CuO4 (LCO) layers. These heterostructures are featured with enhanced ferromagnetism before entering the spin glass state: a Curie temperature of 246 K is observed in the superlattice with six-unit-cell LSMO layers, while the reference LSMO film with the same thickness shows much weaker magnetism. Furthermore, an insulator-metal transition emerges at the Curie temperature, and below the freezing temperature the superlattices can be considered as a glassy ferromagnetic insulator. These experimental results are closely related to the interfacial spin reconstruction revealed by the first-principles calculations, and the dependence of the reentrant spin glass behavior on the LSMO layer thickness is in line with the general phase diagram of a spin system derived from the infinite-range SK model. The results of this work underscore the manganite/cuprate superlattices as a versatile platform of creating artificial materials with tailored interfacial spin coupling and physical properties. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Roberto Viana, J.; Rodriguez Salmon, Octavio D.; Neto, Minos A.; Carvalho, Diego C.
2018-02-01
A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.
Boekema, C.; Brabers, V.A.M.; Lichti, R.L.; Denison, A.B.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Schillaci, M.E.; MacLaughlin, D.E.; Dodds, S.A.
1986-01-01
Zero-field longitudinal muon-spin-relaxation (µSR) experiments have been performed on single crystals of pseudo-brookite (Fe2-xTil+x O 5; x=0.25), an anisotropic spin-glass system. The spinglass temperature (Tg) is determined to be 44.0±0.5K. Above Tg, a distinct exponential muon-spin-relaxation
Aging, rejuvenation and memory phenomena in spin glasses
Indian Academy of Sciences (India)
Spin glass; relaxation; aging; rejuvenation; memory. PACS Nos 75.10. .... the application of finite excitations, the long time needed to cool the sample down ..... wait at T − ∆T during t2 = 9000 s and finally re-heated to T for another short time t3 ...
Magnetoresistance in spin glass alloys: Theory and experiment
International Nuclear Information System (INIS)
Mookerjee, A.; Chowdhury, D.
1984-11-01
The magnetoresistance of spin glass alloys is examined within the percolation model of Mookerjee and Chowdhury (1983), the mode freezing model of Hertz (1983) and the constrained relaxation model of Palmer et al. (1984). All three models yield qualitatively similar results in excellent agreement with the experiments of Majumdar (1983, 1984) on AgMn. (author)
Manganite/Cuprate Superlattice as Artificial Reentrant Spin Glass
Ding, Junfeng; Cossu, Fabrizio; Lebedev, Oleg I.; Zhang, Yuqin; Zhang, Zhidong; Schwingenschlö gl, Udo; Wu, Tao
2016-01-01
magnetic memory effect discovered in oxide heterostructures composed of ultrathin manganite La0.7Sr0.3MnO3 (LSMO) and cuprate La2CuO4 (LCO) layers. These heterostructures are featured with enhanced ferromagnetism before entering the spin glass state: a
Temperature dependence of fluctuation time scales in spin glasses
DEFF Research Database (Denmark)
Kenning, Gregory G.; Bowen, J.; Sibani, Paolo
2010-01-01
Using a series of fast cooling protocols we have probed aging effects in the spin glass state as a function of temperature. Analyzing the logarithmic decay found at very long time scales within a simple phenomenological barrier model, leads to the extraction of the fluctuation time scale of the s...
The pseudo‐brookite spin‐glass system studied by means of muon spin relaxation
Brabers, V.A.M.; Boekema, C.; Lichti, R.L.; Denison, A.B.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Schillaci, M.E.; MacLaughlin, D.E.
1987-01-01
Zero-field muon spin relaxation (µSR) experiments have been performed on the spin glass Fe1.75Ti1.25O5. Above the spin-glass temperature of 44 K a distinct exponential µSR rate (¿) is observed, while below Tg a square-root exponential decay occurs, indicating fast spin fluctuations. Near 8 K, a
International Nuclear Information System (INIS)
Dudek, J.
1989-01-01
The concept of a ''universal'' average field as a basis of intrinsic-frame nuclear physics is stressed. The symmetries of such an average field are discussed. As an important application, an overwiew is given of the recent progress in understanding the octupole-type (intrinsic-parity breaking) degrees of freedom in nuclei. Their importance and the new consequences resulting from the related symmetries and spontaneous symmetry breaking phenomena are emphasized: the presence of static and/or dynamic isovector deformations and their implications, the possible low-energy E1 cooling in moderately hot nuclei at high spins, possible new forms of rotational dumping effects in rotating nuclei etc
Size and field effect on mesoscopic spin glass
Energy Technology Data Exchange (ETDEWEB)
Komatsu, K. [Department of Applied Physics and Physico-Infomatics, Faculty of Science and Technology, Keio University, Yokohama 223-8522 (Japan)]. E-mail: komatsu@az.appi.keio.ac.jp; Maki, H. [Department of Applied Physics and Physico-Infomatics, Faculty of Science and Technology, Keio University, Yokohama 223-8522 (Japan); Taniyama, T. [Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503 (Japan); Sato, T. [Department of Applied Physics and Physico-Infomatics, Faculty of Science and Technology, Keio University, Yokohama 223-8522 (Japan)
2007-03-15
Spin glass particles were prepared as the mesoscopic system in order to examine the space scale of spin glass domain (droplet). The peak temperature T {sub peak} in the temperature-dependent magnetization is systematically reduced with decreasing average particle size. This is due to the imitation of droplet growth to the particle diameter. The magnetic field H also decreases T {sub peak}, which is caused by the reduction of the barrier height by Zeeman energy. However, there appears different tendency in the relation between H and T {sub peak} below 100 Oe. This indicates the existence of crossover between the two regimes in which the free energy and Zeeman energy govern the droplet excitation.
Field-theoretical description of itinerant spin glasses
International Nuclear Information System (INIS)
Kolley, E.; Kolley, W.
1986-01-01
By means of functional integral technique at T 0 the disordered Hubbard model is bosonized, resulting in an effective action of the Ginzburg-Landau type. The quenched-averaged free energy of the itinerant spin glass is calculated by using the replica trick and Bogolyubov's variational principle. The spinglass order parameter and the local magnetic moment fulfil a system of self-consistent equations in the presence of spatial fluctuations. (author)
Population annealing: Theory and application in spin glasses
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.
2015-01-01
Population annealing is an efficient sequential Monte Carlo algorithm for simulating equilibrium states of systems with rough free energy landscapes. The theory of population annealing is presented, and systematic and statistical errors are discussed. The behavior of the algorithm is studied in the context of large-scale simulations of the three-dimensional Ising spin glass and the performance of the algorithm is compared to parallel tempering. It is found that the two algorithms are similar ...
Exploring the dynamics about the glass transition by muon spin relaxation and muon spin rotation
International Nuclear Information System (INIS)
Bermejo, F J; Bustinduy, I; Cox, S F J; Lord, J S; Cabrillo, C; Gonzalez, M A
2006-01-01
The capability of muon spin rotation and muon spin relaxation to explore dynamics in the vicinity of the glass transition is illustrated by results pertaining to three materials exhibiting two different glass-forming abilities. Measurements under transverse magnetic fields enable us to monitor the dynamics of muonium-labelled closed-shell molecules within the microsecond range. The results display the onset of stochastic molecular motions taking place upon crossing from below the glass-transition temperature. In turn, the molecular dynamics of radicals formed by addition of atomic muonium to unsaturated organic molecules can also be explored up to far shorter times by means of relaxation measurements under longitudinal fields. The technique is then shown to be capable of singling out stochastic reorientational motions from others, which usually are strongly coupled to them and usually dominate the material response when measured using higher-frequency probes such as neutron and light scattering
Band mixing effects in mean field theories
International Nuclear Information System (INIS)
Kuyucak, S.; Morrison, I.
1989-01-01
The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs
Relationship between energy landscape and low-temperature dynamics of ±J spin glasses
International Nuclear Information System (INIS)
Kobe, S.; Krawczyk, J.
2004-01-01
Clusters and valleys in the exact low-energy landscape of finite Edwards-Anderson ±J spin glasses are related to the distribution of spin domains and free spins in the ground states. The time evolution of the spin correlation function reflects a walk through the landscape at a given temperature and shows typical glassy behaviour
Experimental study of mixed ferromagnetic spin glass systems
International Nuclear Information System (INIS)
Mirebeau, I.
1987-01-01
The mixed ferromagnetic spin glass systems are characterized by a distribution of positive and negative exchange interactions whose maximum occurs at a positive value. We have undertaken an experimental study of amorphous (Fe 1-x Mn x ) .75 PBA1, polycrystalline and monocrystalline Ni 1-x Mn x and Au 1-x Fe x alloys. By Moessbauer effect, magnetization and neutron scattering, we show that below a ''canting'' temperature T K , spin components transverse to the mean magnetization become frozen. Small angle neutron scattering studies with an applied field show a magnetic ''structure'' i.e. the intensity exhibits a maximum at a finite q value for temperatures below T K . This structure has been studied as a function of temperature, applied field and concentration using both small angle neutron scattering and 3 axis spectrometry where we separate the elastic from the inelastic components. Possible interpretations of this new structure will be given [fr
Legendre Duality of Spherical and Gaussian Spin Glasses
International Nuclear Information System (INIS)
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
Strange attractor in the Potts spin glass on hierarchical lattices
Energy Technology Data Exchange (ETDEWEB)
Lima, Washington de [Universidade Federal de Pernambuco, Centro Acadêmico do Agreste, Pernambuco (Brazil); Camelo-Neto, G. [Universidade Federal de Alagoas, Núcleo de Ciências Exatas, Laboratório de Física Teórica e Computacional, CEP 57309-005 Arapiraca, Alagoas (Brazil); Coutinho, S., E-mail: sergio@ufpe.br [Universidade Federal de Pernambuco, Departamento de Física, Laboratório de Física Teórica e Computacional, Cidade Universitária, CEP 50670-901 Recife, Pernambuco (Brazil)
2013-11-29
The spin-glass q-state Potts model on d-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension d{sub l}(q) for q>2, the coupling constants probability distribution flows to a low-temperature strange attractor or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature T{sub c}(q,d). The strange attractor was investigated considering four initial different distributions for q=3 and d=5 presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.
Legendre Duality of Spherical and Gaussian Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Dynamical TAP equations for non-equilibrium Ising spin glasses
DEFF Research Database (Denmark)
Roudi, Yasser; Hertz, John
2011-01-01
We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
Hyperscaling breakdown and Ising spin glasses: The Binder cumulant
Lundow, P. H.; Campbell, I. A.
2018-02-01
Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric
Quantum spin-glass transition in the two-dimensional electron gas
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 58; Issue 2 ... Spin glasses; quantum phase transition; ferromagnetism; electron gas. ... We argue that a quantum transition involving the destruction of the spin-glass order in an applied in-plane magnetic ﬁeld offers a natural explanation of some features of recent ...
International Nuclear Information System (INIS)
Guerra, E.M. de
2001-01-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
Reentrant spin glass ordering in an Fe-based bulk metallic glass
Energy Technology Data Exchange (ETDEWEB)
Luo, Qiang; Shen, Jun, E-mail: junshen@tongji.edu.cn [School of Materials Science and Engineering, Tongji University, Shanghai 201804 (China)
2015-02-07
We report the results of the complex susceptibility, temperature, and field dependence of DC magnetization and the nonequilibrium dynamics of a bulk metallic glass Fe{sub 40}Co{sub 8}Cr{sub 15}Mo{sub 14}C{sub 15}B{sub 6}Er{sub 2}. Solid indication of the coexistence of reentrant spin glass (SG) and ferromagnetic orderings is determined from both DC magnetization and AC susceptibility under different DC fields. Dynamics scaling of AC susceptibility indicates critical slowing down to a reentrant SG state with a static transition temperature T{sub s} = ∼17.8 K and a dynamic exponent zv = ∼7.3. The SG nature is further corroborated from chaos and memory effects, magnetic hysteresis, and aging behavior. We discuss the results in terms of the competition among random magnetic anisotropy and exchange interactions and compare them with simulation predictions.
Noise as a Probe of Ising Spin Glass Transitions
Chen, Zhi; Yu, Clare
2009-03-01
Noise is ubiquitous and and is often viewed as a nuisance. However, we propose that noise can be used as a probe of the fluctuations of microscopic entities, especially in the vicinity of a phase transition. In recent work we have used simulations to show that the noise increases in the vicinity of phase transitions of ordered systems. We have recently turned our attention to noise near the phase transitions of disordered systems. In particular, we are studying the noise near Ising spin glass transitions using Monte Carlo simulations. We monitor the system as a function of temperature. At each temperature, we obtain the time series of quantities characterizing the properties of the system, i.e., the energy and magnetization. We look at different quantities, such as the noise power spectrum and the second spectrum of the noise, to analyze the fluctuations.
Superexchange and spin-glass formation in semimagnetic semiconductors
Rusin, Tomasz M.
1996-05-01
The Mn-Mn superexchange interaction in semimagnetic semiconductors A1-xMnxB (where A=Zn, Cd and B=S, Se, Te) is studied within the three-level model of the band structure. We focus on the dependence of the interaction on the interion distance Jdd(r)=J0f(r). In the present work, the function f(r) is obtained analytically. This, only weakly material-dependent function is found to decrease with Mn-Mn distance much slower than its Gaussian approximation derived previously. The exact form of the decay of the superexchange can be approximated by a power law J0r-8.5. This is close to an experimental result, J0r-6.8, determined on the basis of the spin-glass transition temperature on the composition.
Ferromagnetism and spin glass ordering in transition metal alloys (invited)
Crane, S.; Carnegie, D. W., Jr.; Claus, H.
1982-03-01
Magnetic properties of transition metal alloys near the percolation threshold are often complicated by metallurgical effects. Alloys like AuFe, VFe, CuNi, RhNi, and PdNi are in general not random solid solutions but have various degrees of atomic clustering or short-range order (SRO), depending on the heat treatment. First, it is shown how the magnetic ordering temperature of these alloys varies with the degree of clustering or SRO. Second, by systematically changing this degree of clustering or SRO, important information can be obtained about the magnetic phase diagram. In all these alloys below the percolation limit, the onset of ferromagnetic order is probably preceded by a spin glass-type ordering. However, details of the magnetic phase diagram near the critical point can be quite different alloy systems.
Muon spin relaxation measurements of the fluctuation modes in spin-glass AgNm
Energy Technology Data Exchange (ETDEWEB)
Heffner, R.H.; Leon, M.; Schillaci, M.E.; MacLaughlin, D.E.; Dodds, S.A.
1983-01-01
Recently reported zero-field ..mu..SR measurements below the spin-glass transition temperature in AgMn (1.6 at%) show a temperature dependent inhomogeneous width. The authors discuss these data in terms of a model in which the local field undergoes limited-amplitude fluctuations. The authors find that both very slow (approx. = 0.3 ..mu..s/sup -1/) and rapid (approx. = 3000 ..mu..s/sup -1/) fluctuations are required. 10 references, 1 figure, 1 table.
On modeling of statistical properties of classical 3D spin glasses
International Nuclear Information System (INIS)
Gevorkyan, A.S.; Abajyan, H.G.; Ayryan, E.A.
2011-01-01
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin chains (SSC) where interactions are random between spin chains (nonideal ensemble of 1D SSCs). It is proved that in the limit of Birkhoff's ergodic hypothesis performance, 3D spin glasses can be generated by Hamiltonian of disordered 1D SSC with random environment. Disordered 1D SSC is defined on a regular lattice where one randomly oriented spin is put on each node of lattice. Also, it is supposed that each spin randomly interacts with six nearest-neighboring spins (two spins on lattice and four in the environment). The recurrent transcendental equations are obtained on the nodes of spin-chain lattice. These equations, combined with the Silvester conditions, allow step-by-step construction of spin chain in the ground state of energy where all spins are in the minimal energy of a classical Hamiltonian. On the basis of these equations an original high-performance parallel algorithm is developed for 3D spin glasses simulation. Distributions of different parameters of unperturbed spin glass are calculated. In particular, it is analytically proved and numerical calculations show that the distribution of spin-spin interaction constant in Heisenberg nearest-neighboring Hamiltonian model, as opposed to widely used Gauss-Edwards-Anderson distribution, satisfies the Levy alpha-stable distribution law which does not have variance. A new formula is proposed for construction of partition function in the form of a one-dimensional integral on the energy distribution of 1D SSCs
Kato, Tomohiko; Saita, Takahiro
2011-03-16
The magnetism of Pd(1-x)Mn(x) is investigated theoretically. A localized spin model for Mn spins that interact with short-range antiferromagnetic interactions and long-range ferromagnetic interactions via itinerant d electrons is set up, with no adjustable parameters. A multicanonical Monte Carlo simulation, combined with a procedure of symmetry breaking, is employed to discriminate between the ferromagnetic and spin glass orders. The transition temperature and the low-temperature phase are determined from the temperature variation of the specific heat and the probability distributions of the ferromagnetic order parameter and the spin glass order parameter at different concentrations. The calculation results reveal that only the ferromagnetic phase exists at x glass phase exists at x > 0.04, and that the two phases coexist at intermediate concentrations. This result agrees semi-quantitatively with experimental results.
Zero-field NMR study on a spin glass: iron-doped 2H-niobium diselenide
International Nuclear Information System (INIS)
Chen, M.C.
1982-01-01
Spin echoes are used to study the 93 Nb NQR in 2H-NbSe 2 Fe/sub x/. Measured are (intensity) x (temperature), and T/sub 1P/ (spin-lattice relaxation parameter) and T 2 (spin-spin relaxation time) as a function of temperature. Data reveal dramatic differences between non-spin glass samples (x = 0, 0.25%, 1% and 5%) and spin glass samples (x = 8%, 10% and 12%). All of the NQR results and the model calculation of the correlation times of Fe spins are best described by the phase transition picture of spin glasses
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Spin freezing in the re-entrant spin glass FeNiMn close to the frustration limit
Energy Technology Data Exchange (ETDEWEB)
Pappas, Catherine [Hahn-Meitner-Institut, Glienickerstr. 100, 14109 Berlin (Germany); Klenke, Jens [Hahn-Meitner-Institut, Glienickerstr. 100, 14109 Berlin (Germany); Hesse, Juergen [Institut fuer Metallphysik und Nukleare Festkoerperphysik, Technische Universitaet Braunschweig, 38106 Braunschweig (Germany); Wagner, Volker [Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig (Germany)]. E-mail: volker.wagner@ptb.de
2007-07-15
In the invar alloy (Fe{sub 0.65}Ni{sub 0.35}){sub 1-} {sub x} Mn {sub x} we measured the magnetic form factor s(Q) and the intermediate scattering function s(Q,t) for a sample close to the critical Mn concentration (x {sub c}=0.139), at which the sample turns to a re-entrant spin glass phase. The aim was to check whether the magnetic behaviour would approach the Q-independent relaxation behaviour of a classical spin glass when x=x {sub c}. The experiment showed a quite similar spin freezing as for a more ferromagnetic sample with x=0.113. The intermediate scattering function and the form factor were determined by paramagnetic NSE. The normalized scattering function S(Q,t)=s(Q,t)/s(Q)=exp[(-{gamma}t) {sup n}] was fitted by stretched exponential decay. As a function of temperature T<200 K the inverse time constant {gamma} showed the change of more than four orders of magnitude from frozen spin glass (T=60 K to T=100 K), where the ferromagnetic phase occurred. In general, the inverse time constant is higher than in the more ferromagnetic sample as the frustration of the spins became larger. In the ferromagnetic phase S(Q,t) depended on 0.3spin diffusive behaviour remained in the re-entrant spin glass down to at least 60 K.
Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
Directory of Open Access Journals (Sweden)
Giulio Biroli, Charlotte Rulquin, Gilles Tarjus, Marco Tarzia
2016-10-01
Full Text Available We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas of the system. We consider both short-range fluctuations associated with the local environment on Bethe lattices and long-range fluctuations that distinguish Euclidean from Bethe lattices with the same local environment. We find that the phase diagram in the temperature-coupling plane is very sensitive to the former but, at least for the $3$-dimensional (square pyramid model, appears qualitatively or semi-quantitatively unchanged by the latter. This surprising result suggests that the mean-field theory of glasses provides a reasonable account of the glassy thermodynamics of models otherwise described in terms of the kinetically constrained motion of localized defects and taken as a paradigm for the theory of dynamic facilitation. We discuss the possible implications for the dynamical behavior.
Low-field susceptibilities of rare-earth spin glass alloys
International Nuclear Information System (INIS)
Sarkissian, B.V.B.
1978-01-01
The low-field AC susceptibilities of the dilute rare-earth spin glass alloys Sc-Gd, Sc-Tb, Pr-Tb and Pr-Gd are reported and compared with low-field DC susceptibilities of the same samples. The similarities between their behaviour and that of Au-Fe spin glass alloys is also considered. When single-ion anisotropy is important, this can cause a dramatic broadening of the sharp peak. Broadening in the AC peak has also observed as the frequency of the deriving field is increased. These data can be qualitatively discussed in terms of a recent magnetic-cluster model for spin glasses. (author)
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Stability and replica symmetry in the ising spin glass: a toy model
International Nuclear Information System (INIS)
De Dominicis, C.; Mottishaw, P.
1986-01-01
Searching for possible replica symmetric solutions in an Ising spin glass (in the tree approximation) we investigate a toy model whose bond distribution has two non vanishing cumulants (instead of one only as in a gaussian distribution)
Physical Properties of AR-Glass Fibers in Continuous Fiber Spinning Conditions
Energy Technology Data Exchange (ETDEWEB)
Lee, Ji-Sun; Lee, MiJai; Lim, Tae-Young; Lee, Youngjin; Jeon, Dae-Woo; Kim, Jin-Ho [Korea Institute of Ceramic Engineering and Technology, Jinju (Korea, Republic of); Hyun, Soong-Keun [Inha University, Incheon (Korea, Republic of)
2017-04-15
In this study, a glass fiber is fabricated using a continuous spinning process from alkali resistant (AR) glass with 4 wt%zirconia. In order to confirm the melting properties of the marble glass, the raw material is placed into a Pt crucible and melted at 1650 ℃ for 2 h, and then annealed. In order to confirm the transparency of the clear marble glass, the visible transmittance is measured and the fiber spinning condition is investigated by using high temperature viscosity measurements. A change in the diameter is observed according to the winding speed in the range of 100–900 rpm; it is also verified as a function of the fiberizing temperature in the range of 1200–1260 ℃. The optimum winding speed and spinning temperature are 500 rpm and 1240 ℃, respectively. The properties of the prepared spinning fiber are confirmed using optical microscope, tensile strength, modulus, and alkali-resistant tests.
Dynamical Properties of a Diluted Dipolar-Interaction Heisenberg Spin Glass
International Nuclear Information System (INIS)
Zhang Kai-Cheng; Liu Yong; Chi Feng
2014-01-01
Up to now the chirality is seldom studied in the diluted spin glass although many investigations have been performed on the site-ordered Edwards—Anderson model. By simulation, we investigate the dynamical properties of both the spin-glass and the chiral-glass phases in a diluted dipolar system, which was manifested to have a spin-glass transition by recent numerical study. By scaling we find that both phases have the same aging behavior and closer aging parameter μ. Similarly, the domains grow in the same way and both phases have a closer barrier exponent Ψ. It means that both the spins and the chirality have the same dynamical properties and they may freeze at the same temperature. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Exact properties of spin glasses. I. 2D supersymmetry and Nishimori's result
International Nuclear Information System (INIS)
Georges, A.; Le Doussal, P.; Hansel, D.
1985-01-01
We introduce an effective theory of interacting fermions and bosons in order to express the quenched internal energy of the 2D Ising spin glass. We show that an exact result derived by Nishimori appears, in this formulation, as a dimensional reduction due to the apparition of a supersymmetry. For a general Ising spin glass, this suggests new insights into the physical meaning of this exact result
Spin-glass in low dimension and the Midgal Kadanoff approximation
International Nuclear Information System (INIS)
Curado, E.M.F.
1987-01-01
We study the spin glass problem within the Migdal Kadanoff approximation of the hyper cubic lattices. Using various technics, both analytical and numerical, we perform the real space renormalization of the problem. We find that a Spin Glass transition occurs in 3 dimensions while it does not occur in two dimensions. The specific heat critical exponent for the transition is found to be large and negative in agreement with the experimental results. (author) [pt
Sen, S.; Stebbins, J. F.
1994-07-01
A comparative study of the 29Si spin-lattice relaxation behavior (induced by trace amounts of paramagnetic dopants in the glass) in phase-separated Li2Si4O9 and monophasic Li2Si2O5 and Na2Si2O5 glasses has been made in order to understand the nature of clustering and the resulting intermediate-range ordering. Optically clear tetrasilicate and disilicate glasses were prepared with 500 to 2000 ppm of Gd2O3, a paramagnetic dopant. The constituent structural units (Q3 and Q4 species) in all tetrasilicate glasses show strong differential relaxation following a power-law behavior. This is due to preferential partitioning of Gd3+ into the lower silica (Q3-rich) regions of these glasses, indicating the presence of Q species clusters too small to produce optical opalescence (a few nm to perhaps tens of nm). Preliminary results on 6Li spin-lattice relaxation in these glasses support this hypothesis. Differential relaxation becomes more pronounced on annealing due to growth of such clusters. No such differential relaxation was observed in the monophase disilicate glasses. For spin-lattice relaxation induced by direct dipolar coupling to paramagnetic ions, the recovery of magnetization is proportional to time as M(t)~tα where α is a function of the dimensionality D of mass distribution of the constituent Q species around the Gd3+ paramagnetic centers in the glass. For tetrasilicate glasses D~=2.62+/-0.22 and the system behaves as a mass fractal up to a length scale of 2 to 3 nm. D is thus equal to, within error, the theoretical value of 2.6 for an infinite percolation cluster of one type of Q species in another. For disilicate glasses, D~=3.06+/-0.18 which indicates a three-dimensional (and thus nonfractal) mass distribution of the constituent Q species over the same length scale.
International Nuclear Information System (INIS)
Sanpera, A.; Lewenstein, M.; Kantian, A.; Sanchez-Palencia, L.; Zakrzewski, J.
2004-01-01
We investigate strongly interacting atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. We derive an effective Hamiltonian for the system and discuss its low temperature physics. We demonstrate the possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin-glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices
International Nuclear Information System (INIS)
Crisanti, Andrea; Leuzzi, Luca
2013-01-01
We report some results on the quenched disordered Spherical multi-p-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous–amorphous transitions and spin–glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information
Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
International Nuclear Information System (INIS)
Annibale, Alessia; Gualdi, Giulia; Cavagna, Andrea
2004-01-01
The structure of states of the perturbed p-spin spherical spin-glass is analysed. At low enough free energy, metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states
Mean field interaction in biochemical reaction networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2011-01-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits
Low temperature spin-glass-like phases in magnetic nano-granular composites
Zhang, Bei
2012-09-01
It is a common understanding that the dipole-dipole interaction among the magnetic nanoparticles may result in a low-temperature spin-glass phase, which has been evidenced by observation of aging effect and memory effect. However, several studies on the nano-particles systems showed that some of the observed spin-glass-like phenomena could be due to the existence of spin-glasslike shells surrounding the ferrimagnetic cores. Therefore, it is very important to understand that how the dipole-dipole interaction induce the spin-glass phase. In order to address this issue, we have fabricated Co-SiO 2 and Fe-SiO 2 nano-granular thin films and measured the memory effect for them. Spin-glass-like phase has been observed at low temperatures. We found that, after annealing, the size of the clusters increased significantly. Based on a simple model, the dipole-dipole interaction between the clusters must be increased accordingly for the annealed samples. Interestingly, the memory effect is greatly weakened in the annealed films, which strongly suggested that the dipole-dipole interaction may not be the major factor for the formation of the low-temperature spin-glass-like phase. Copyright © 2012 American Scientific Publishers All rights reserved.
Boukahil, A.; Huber, D. L.
1989-09-01
The harmonic magnon modes in a one-dimensional Heisenberg spin glass having nearest-neighbor exchange interactions of fixed magnitude and random sign are investigated. The Lyapounov exponent is calculated for chains of 107-108 spins over the interval 0Stinchcombe and Pimentel using transfer-matrix techniques; at higher frequencies, gaps appear in the spectrum. At low frequencies, the localization length diverges as ω-2/3. A formal connection is established between the spin glass and the one-dimensional discretized Schrödinger equation. By making use of the connection, it is shown that the theory of Derrida and Gardner, which was developed for weak potential disorder, can account quantitatively for the distribution and localization of the low-frequency magnon modes in the spin-glass model.
Evolution of ferromagnetic interactions from cluster spin glass state in Co–Ga alloy
Energy Technology Data Exchange (ETDEWEB)
Mohammad Yasin, Sk. [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India); Saha, Ritwik [Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005 (India); Srinivas, V., E-mail: veeturi@iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India); Kasiviswanathan, S. [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India); Nigam, A.K. [Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005 (India)
2016-11-15
Low temperature magnetic properties of binary Co{sub x}Ga{sub 100−x} (x=54–57) alloy have been investigated. Analysis of frequency dependence of ac susceptibility provided a conclusive evidence for the existence of cluster spin glass like behavior with the freezing temperature ~8, 14 K for x=54, 55.5 respectively. The parameters for conventional ‘slowing down’ of the spin dynamics have been extracted from the acs data, which confirm the presence of glassy phase. The magnitude of Mydosh parameter obtained from the fits is larger than that reported for typical canonical spin glasses and smaller than those for non-interacting ideal superparamagnetic systems but comparable to those of known cluster-glass systems. Memory phenomena using specific cooling protocols also support the spin-glass features in Co{sub 55.5}Ga{sub 44.5} composition. Further the development of ferromagnetic clusters from the cluster spin glass state has been observed in x=57 composition. - Highlights: • Temperature dependence of DC and AC susceptibility (acs) analysis has been carried out on Co{sub x}Ga{sub 1−x,} (x=54–57). • M–H data above transition suggests presence of spin clusters. • A detailed analysis of acs data suggests a cluster glass behavior as oppose to SPM state for x=54 and 55.5. • Memory phenomena using specific cooling protocols also support the spin-glass features in Co{sub 55.5}Ga{sub 44.5} composition. • Development of ferromagnetic like behavior for x≥57 has been suggested from DC and AC magnetization data.
Environment overwhelms both nature and nurture in a model spin glass
Middleton, A. Alan; Yang, Jie
We are interested in exploring what information determines the particular history of the glassy long term dynamics in a disordered material. We study the effect of initial configurations and the realization of stochastic dynamics on the long time evolution of configurations in a two-dimensional Ising spin glass model. The evolution of nearest neighbor correlations is computed using patchwork dynamics, a coarse-grained numerical heuristic for temporal evolution. The dependence of the nearest neighbor spin correlations at long time on both initial spin configurations and noise histories are studied through cross-correlations of long-time configurations and the spin correlations are found to be independent of both. We investigate how effectively rigid bond clusters coarsen. Scaling laws are used to study the convergence of configurations and the distribution of sizes of nearly rigid clusters. The implications of the computational results on simulations and phenomenological models of spin glasses are discussed. We acknowledge NSF support under DMR-1410937 (CMMT program).
Relativistic mean field theory for unstable nuclei
International Nuclear Information System (INIS)
Toki, Hiroshi
2000-01-01
We discuss the properties of unstable nuclei in the framework of the relativistic mean field (RMF) theory. We take the RMF theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted from the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter sets (TM1 and TMA) is promising in comparison with various experimental data. We calculate systematically the ground state properties of even-even nuclei up to the drip lines; about 2000 nuclei. We find that the neutron magic shells (N=82, 128) at the standard magic numbers stay at the same numbers even far from the stability line and hence provide the feature of the r-process nuclei. However, many proton magic numbers disappear at the neutron numbers far away from the magic numbers due to the deformations. We discuss how to describe giant resonances for the case of the non-linear coupling terms for the sigma and omega mesons in the relativistic RPA. We mention also the importance of the relativistic effect on the spin observables as the Gamow-Teller strength and the longitudinal and transverse spin responses. (author)
Correlation between magnetoresistance and magnetization in Ag Mn and Au Mn spin glasses
International Nuclear Information System (INIS)
Majumdar, A.K.
1982-08-01
Magnetization has been measured between 2 and 77 K and mostly up to fields of 20 K Oe in Ag Mn (1.1 and 5.4 at %) and Au Mn (1.8 and 4.6 at %) spin glass samples where the transverse magnetoresistance was measured earlier. It is found for the first time over a wide range of temperature and magnetic field that the negative magnetoresistance varies as the square of the bulk magnetization resulting in an universal curve in the spin glass regime. A theoretical justification is provided in terms of exciting theories. (author)
International Nuclear Information System (INIS)
Bernard, Denis; Le Doussal, Pierre; Middleton, A. Alan
2007-01-01
Domain walls for spin glasses are believed to be scale invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE κ . Multiple tests are consistent with SLE κ , where κ=2.32±0.08. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit
Glass transition in the spin-density wave phase of (TMTSF)2PF6
DEFF Research Database (Denmark)
Lasjaunias, J.C.; Biljakovic, K.; Nad, F.
1994-01-01
We present the results of low frequency dielectric measurements and a detailed kinetic investigation of the specific heat anomaly in the spin-density wave phase of (TMTSF)(2)PF6 in the temperature range between 2 and 4 K. The dielectric relaxation shows a critical slowing down towards a ''static'......'' glass transition around 2 K. The jump in the specific heat in different controlled kinetic conditions shows all the characteristics of freezing in supercooled liquids. Both effects give direct evidence of a glass transition in the spin-density wave ground state....
A novel approach to modelling non-exponential spin glass relaxation
Energy Technology Data Exchange (ETDEWEB)
Pickup, R.M. [School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom)]. E-mail: r.cywinski@leeds.ac.uk; Cywinski, R. [School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom); Pappas, C. [Hahn-Meitner Institut, Glienicker Strasse 100, 14109 Berlin (Germany)
2007-07-15
A probabilistic cluster model, originally proposed by Weron to explain the universal power law of dielectric relaxation, is shown to account for the non-exponential relaxation in spin glasses above T {sub g}. Neutron spin echo spectra measured for the cluster glass compound Co{sub 55}Ga{sub 45} are well described by the Weron relaxation function, {phi}(t)={phi} {sub o}(1+k(t/{tau}) {sup {beta}}){sup -1/k}, with the interaction parameter k scaling linearly with the non-Curie-Weiss susceptibility.
Memory effect and super-spin-glass ordering in an aggregated nanoparticle sample
International Nuclear Information System (INIS)
Cador, O.; Grasset, F.; Haneda, H.; Etourneau, J.
2004-01-01
A system consisting of aggregated nonstoichiometric zinc ferrite nanoparticles has been studied using AC and DC magnetization measurements. A superparamagnetic-super-spin-glass phase transition at T g has been identified. The relaxation time diverges at T g and the nonlinear susceptibility shows an abrupt increase. The critical behavior vanishes when the nanoparticles are not in close contact. The observation of the memory effect identical to that which has been already discovered in canonical spin-glass supports the existence of a true thermodynamic transition in agglomerated magnetic nanoparticles
Absence of aging in the remanent magnetization in Migdal-Kadanoff spin glasses
International Nuclear Information System (INIS)
Ricci-Tersenghi, F.; Ritort, F.
2000-04-01
We study the non-equilibrium behavior of three-dimensional spin glasses in the Migdal-Kadanoff approximation. This approximation is exact for disordered hierarchical lattices which have a unique ground state and equilibrium properties correctly described by the droplet model. Extensive numerical simulations show that this model lacks aging in the remanent magnetization as well as a maximum in the magnetic viscosity in disagreement with experiments as well as with numerical studies of the Edwards-Anderson model. This result strongly limits the validity of the droplet model (at least in its simplest form) as a good model for real spin glasses. (author)
International Nuclear Information System (INIS)
Oppermann, R.; Rosenow, B.
1997-10-01
We report large effects of Parisi replica permutation symmetry breaking (RPSB) on elementary excitations of fermionic systems with frustrated magnetic interactions. The electronic density of states is obtained exactly in the zero temperature limit for (K = 1)- step RPSB together with relations for arbitrary breaking K, which lead to a new fermionic and dynamical Parisi solution at K = ∞. The Ward identity for charge conservation indicates RPSB-effects on the conductivity in metallic quantum spin glasses. This implies that RPSB is essential for any fermionic system showing spin glass sections within its phase diagram. An astonishing similarity with a neural network problem is also observed. (author)
Zero and finite field μSR spin glass Ag:Mn
International Nuclear Information System (INIS)
Brown, J.A.; Heffner, R.H.; Leon, M.; Olsen, C.E.; Schillaci, M.E.; Dodds, S.A.; Estle, T.L.; MacLaughlin, D.E.
1981-01-01
In this paper we present μSR data taken in both zero and finite fields for a Ag:Mn (1.6 at%) spin glass sample. The data allow us to determine, in the context of a particular model, the fluctuation rate of the Mn ions as a function of temperature. This rate decreases smoothly but very rapidly near the glass temperature, Tsub(g). The corresponding behavior in Cu:Mn is more gradual. (orig.)
Explorations on High Dimensional Landscapes: Spin Glasses and Deep Learning
Sagun, Levent
This thesis deals with understanding the structure of high-dimensional and non-convex energy landscapes. In particular, its focus is on the optimization of two classes of functions: homogeneous polynomials and loss functions that arise in machine learning. In the first part, the notion of complexity of a smooth, real-valued function is studied through its critical points. Existing theoretical results predict that certain random functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This section provides empirical evidence for convergence of gradient descent to local minima whose energies are near the predicted threshold justifying the existing asymptotic theory. Moreover, it is empirically shown that a similar phenomenon may hold for deep learning loss functions. Furthermore, there is a comparative analysis of gradient descent and its stochastic version showing that in high dimensional regimes the latter is a mere speedup. The next study focuses on the halting time of an algorithm at a given stopping condition. Given an algorithm, the normalized fluctuations of the halting time follow a distribution that remains unchanged even when the input data is sampled from a new distribution. Two qualitative classes are observed: a Gumbel-like distribution that appears in Google searches, human decision times, and spin glasses and a Gaussian-like distribution that appears in conjugate gradient method, deep learning with MNIST and random input data. Following the universality phenomenon, the Hessian of the loss functions of deep learning is studied. The spectrum is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. Empirical evidence is presented for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data. Furthermore, an algorithm is proposed such that it would
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Spin-glass polyamorphism induced by a magnetic field in LaMnO3 single crystal
Eremenko, V. V.; Sirenko, V. A.; Baran, A.; Čižmár, E.; Feher, A.
2018-05-01
We present experimental evidence of field-driven transition in spin-glass state, similar to pressure-induced transition between amorphous phases in structural and metallic glasses, attributed to the polyamorphism phenomena. Cusp in temperature dependences of ac magnetic susceptibility of weakly disordered LaMnO3 single crystal is registered below the temperature of magnetic ordering. Frequency dependence of the cusp temperature proves its spin-glass origin. The transition induced by a magnetic field in spin-glass state, is manifested by peculiarity in dependence of cusp temperature on applied magnetic field. Field dependent maximum of heat capacity is observed in the same magnetic field and temperature range.
Theory of spin-lattice relaxation of diffusing light nuclei in glasses
International Nuclear Information System (INIS)
Schirmer, A.; Schirmacher, W.
1988-01-01
NMR data of diffusion-induced spin-lattice relaxation in glasses cannot generally be interpreted in the framework of the classical theory of Bloembergen, Purcell and Pound (BPP). Since it is based on exponential density relaxation, generally bnot found in glasses, the BPP formula must be generalized. Here a combination of standard relaxation theory with a hopping model for diffusion in glasses is present. It is shown that the observed anomaties in the NMR data can be explained as a result of anomalous diffusion. 25 refs.; 1 figure
Shapiro, S M; Raymond, S; Lee, S H; Motoya, K
2002-01-01
Fe sub 0 sub . sub 7 Al sub 0 sub . sub 3 is a reentrant spin glass, which undergoes a transition from a paramagnet to a disordered ferromagnet at T sub c propor to 500 K; at a lower temperature the spins progressively freeze and it exhibits a spin-glass-like behavior. In the ferromagnetic phase spin waves with a q sup 2 dispersion are observed at small q, which broaden rapidly and become diffusive beyond a critical wave vector q sub 0. On cooling the spin waves also disappear and a strong elastic central peak develops. For measurements around the (1,1,1) Bragg peak, a new sharp excitation is observed which has a linear dispersion behavior. It disappears above T sub c , but persists throughout the spin-glass phase. It is not present in the stoichiometric Fe sub 3 Al material. (orig.)
Quasi-realistic distribution of interaction fields leading to a variant of Ising spin glass model
International Nuclear Information System (INIS)
Tanasa, Radu; Enachescu, Cristian; Stancu, Alexandru; Linares, Jorge; Varret, Francois
2004-01-01
The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced
Nuclear spin dominated relaxation of atomic tunneling systems in glasses
Energy Technology Data Exchange (ETDEWEB)
Luck, Annina
2016-11-16
The measurements performed in this thesis have revealed a non phononic relaxation channel for atomic tunneling systems in glasses at very low temperatures due to the presence of nuclear electric quadrupoles. Dielectric measurements on the multicomponent glasses N-KZFS11 and HY-1, containing {sup 181}Ta and {sup 165}Ho, respectively, that both carry very large nuclear electric quadrupole moments, show a relaxation rate in the kilohertz range, that is constant for temperatures exceeding the nuclear quadrupole splitting of the relevant isotopes. The results are compared to measurements performed on the glasses Herasil and N-BK7 that both contain no large nuclear quadrupole moments. Using three different setups to measure the complex dielectric function, the measurements cover almost eight orders of magnitude in frequency from 60 Hz to 1 GHz and temperatures down to 7.5 mK. This has allowed us a detailed study of the novel effects observed within this thesis and has led to a simplified model explaining the effects of nuclear electric quadrupoles on the behavior of glasses at low temperatures. Numeric calculations based on this model are compared to the measured data.
Phase Transition in the Density of States of Quantum Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Erdős, László, E-mail: lerdos@ist.ac.at [IST Austria (Austria); Schröder, Dominik, E-mail: schroeder.dominik@gmail.com [Ludwig-Maximilians-Universität München (Germany)
2014-12-15
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n{sup 1/2} we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.
Nature of the spin-glass phase at experimental length scales
International Nuclear Information System (INIS)
Alvarez Baños, R; Cruz, A; Fernandez, L A; Gil-Narvion, J M; Gordillo-Guerrero, A; Maiorano, A; Martin-Mayor, V; Monforte-Garcia, J; Perez-Gaviro, S; Ruiz-Lorenzo, J J; Seoane, B; Tarancon, A; Guidetti, M; Mantovani, F; Schifano, S F; Tripiccione, R; Marinari, E; Parisi, G; Muñoz Sudupe, A; Navarro, D
2010-01-01
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L = 32 lattices down to T ≈ 0.64T c . We demonstrate the relevance of equilibrium finite size simulations to understanding experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a timescale of 1 h can be matched with equilibrium results on L ≈ 110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies in ensuring equilibration in parallel tempering simulations
Spin glasses and nonlinear constraints in portfolio optimization
Energy Technology Data Exchange (ETDEWEB)
Andrecut, M., E-mail: mircea.andrecut@gmail.com
2014-01-17
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
Spin glasses and nonlinear constraints in portfolio optimization
International Nuclear Information System (INIS)
Andrecut, M.
2014-01-01
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
Continuous time finite state mean field games
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Risk-sensitive mean-field games
Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer
2014-01-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Continuous Time Finite State Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Continuous Time Finite State Mean Field Games
International Nuclear Information System (INIS)
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.; Voskanyan, Vardan K.
2016-01-01
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Shapes of tree representations of spin-glass landscapes
International Nuclear Information System (INIS)
Hordijk, Wim; Fontanari, Jose F; Stadler, Peter F
2003-01-01
Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure - a barrier tree - the leaves and internal nodes of which represent, respectively, the local minima and the lowest energy saddles connecting those minima. Here we apply several statistics used in the study of phylogenetic trees to barrier trees that result from the energy landscapes of p-spin models. These statistics give information about the shape of these barrier trees, in particular about balance and symmetry. We then ask if they can be used to classify different types of landscapes, compare them with results obtained from random trees, and investigate the structure of subtrees of the barrier trees. We conclude that at least one of the used statistics is capable of distinguishing different types of landscapes, that the barrier trees from p-spin energy landscapes are quite different from random trees, and that subtrees of barrier trees do not reflect the overall tree structure, but their structure is correlated with their 'depth' in the tree
Relativistic mean-field mass models
Energy Technology Data Exchange (ETDEWEB)
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Analytical evidence for the absence of spin glass transition on self-dual lattices
International Nuclear Information System (INIS)
Ohzeki, Masayuki; Nishimori, Hidetoshi
2009-01-01
We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random-bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four-dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point. (fast track communication)
Quantum Critical Point revisited by the Dynamical Mean Field Theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei
Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.
Quantum critical point revisited by dynamical mean-field theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.
2017-03-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Quantum critical point revisited by dynamical mean-field theory
International Nuclear Information System (INIS)
Xu, Wenhu; Kotliar, Gabriel; Rutgers University, Piscataway, NJ; Tsvelik, Alexei M.
2017-01-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Mean-field models and exotic nuclei
Energy Technology Data Exchange (ETDEWEB)
Bender, M; Buervenich, T; Maruhn, J A; Greiner, W [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); [Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P G [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Mean-field models and exotic nuclei
International Nuclear Information System (INIS)
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W.; Rutz, K.; Reinhard, P.G.
1998-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)
Fictive impurity approach to dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Fictive impurity approach to dynamical mean field theory
International Nuclear Information System (INIS)
Fuhrmann, A.
2006-10-01
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Magnetic surfactants as molecular based-magnets with spin glass-like properties
International Nuclear Information System (INIS)
Brown, Paul; Hatton, T Alan; Smith, Gregory N; Hernández, Eduardo Padrón; James, Craig; Eastoe, Julian; Nunes, Wallace C; Settens, Charles M; Baker, Peter J
2016-01-01
This paper reports the use of muon spin relaxation spectroscopy to study how the aggregation behavior of magnetic surfactants containing lanthanide counterions may be exploited to create spin glass-like materials. Surfactants provide a unique approach to building in randomness, frustration and competing interactions into magnetic materials without requiring a lattice of ordered magnetic species or intervening ligands and elements. We demonstrate that this magnetic behavior may also be manipulated via formation of micelles rather than simple dilution, as well as via design of surfactant molecular architecture. This somewhat unexpected result indicates the potential of using novel magnetic surfactants for the generation and tuning of molecular magnets. (paper)
Spin-glass-like transition in the majority-vote model with anticonformists
Krawiecki, Andrzej
2018-03-01
Majority-vote model on scale-free networks and random graphs is investigated in which a randomly chosen fraction p of agents (called anticonformists) follows an antiferromagnetic update rule, i.e., they assume, with probability governed by a parameter q (0 transition from a disordered (paramagnetic) state to a spin-glass-like state, characterized by a non-zero value of the spin-glass order parameter measuring the overlap of agents' opinions in two replicas of the system, and simultaneously by the magnetization close to zero. In the case of the model on scale-free networks the critical value of the parameter q weakly depends on the details of the degree distribution. As p is decreased, the critical value of q falls quickly to zero and only the disordered phase is observed. On the other hand, for p close to zero for decreasing q the usual ferromagnetic transition is observed.
From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems
Hamze, Firas; Jacob, Darryl C.; Ochoa, Andrew J.; Perera, Dilina; Wang, Wenlong; Katzgraber, Helmut G.
2018-04-01
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1 ,+1 } , are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint-satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.
Probing the chemistry of adhesion between a 316L substrate and spin-on-glass coating
DEFF Research Database (Denmark)
Lampert, Felix; Kadkhodazadeh, Shima; Kasama, Takeshi
2018-01-01
Hydrogen silsesquioxane ([HSiO3/2]n) based "spin-on-glass" has been deposited on 316L substrate and cured in Ar/H2 gas atmosphere at 600 ºC to form a continuous surface coating with sub-micrometer thickness. The coating functionality depends primarily on the adhesion to the substrate, which...... is largely affected by the chemical interaction at the interface between the coating and the substrate. We have investigated this interface by transmission electron microscopy and electron energy loss spectroscopy. The analysis identified a 5-10 nm thick interaction zone containing signals from O, Si, Cr....... In agreement with computational thermodynamics, it is proposed that the spin-on-glass forms a chemically bonded silicate-rich interaction zone with the substrate. It was further suggested that this zone is composed of a corundum-type oxide at the substrate surface, followed by an olivine-structure intermediate...
Spin glass transition in canonical AuFe alloys: A numerical study
International Nuclear Information System (INIS)
Zhang, Kai-Cheng; Li, Yong-Feng; Liu, Gui-Bin; Zhu, Yan
2012-01-01
Although spin glass transitions have long been observed in diluted magnetic alloys, e.g. AuFe and CuMn alloys, previous numerical studies are not completely consistent with the experiment results. The abnormal critical exponents of the alloys remain still puzzling. By employing parallel tempering algorithm with finite-size scaling analysis, we investigated the phase transitions in canonical AuFe alloys. Our results strongly support that spin glass transitions occur at finite temperatures in the alloys. The calculated critical exponents agree well with those obtained from experiments. -- Highlights: ► By simulation we investigated the abnormal critical exponents observed in canonical SG alloys. ► The critical exponents obtained from our simulations agree well with those measured from experiments. ► Our results strongly support that RKKY interactions lead to SG transitions at finite temperatures.
Time independent mean-field theory
International Nuclear Information System (INIS)
Negele, J.W.
1980-02-01
The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures
Spin glass transition in a thin-film NiO/permalloy bilayer
Ma, Tianyu; Urazhdin, Sergei
2018-02-01
We experimentally study magnetization aging in a thin-film NiO/permalloy bilayer. Aging characteristics are nearly independent of temperature below the exchange bias blocking temperature TB, but rapidly vary above it. The dependence on the magnetic history qualitatively changes across TB. The observed behaviors are consistent with the spin glass transition at TB, with significant implications for magnetism and magnetoelectronic phenomena in antiferromagnet/ferromagnet bilayers.
Study of ±J Ising spin glasses via multicanonical ensemble
International Nuclear Information System (INIS)
Celik, T.; Berg, B.
1993-03-01
The authors performed numerical simulations of 2D and 3D Edwards-Anderson spin glass models by using the recently developed multicanonical ensemble. The ergodicity times increase with the lattice size approximately as V 3 . The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored
Electrical resistivity of Y(Fe1-x Alx)2 in the spin glass concentration range
International Nuclear Information System (INIS)
Cunha, S.F. da; Souza, G.P. de; Takeushi, A.Y.
1986-01-01
The temperature dependence of the electrical resistivity of the Y(Fe 1-x Al x ) 2 system (0.125 ≤ x ≤ 0.25) was measured. This system exhibits a minimum at low temperatures for the concentration range where the phase diagram presents a spin glass-ferromagnetic transition. A negative temperature coefficient is observed at high temperatures for x > 0.18 and was attributed to the high value of the electrical resistivity in this concentration range. (Author) [pt
Relaxor behavior in spin glass perovskite Sr2CoRuO6
International Nuclear Information System (INIS)
Phatak, Rohan; Sali, S.K.; Mishra, S.K.; Das, A.
2014-01-01
Dielectric properties of Sr 2 CoRuO 6 perovskite have been investigated. The compound crystallizes in monoclinic I2/c space group, with random distribution of Co and Ru ion on B site. From our previous study, we showed this compound to be magnetic spin glass with transition at 95K, and was investigated using neutron diffraction and depolarization, ac magnetization and time dependent magnetization
Singh, R. R. P.; Young, A. P.
2017-08-01
We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.
Observation of spin-glass behavior in nickel adsorbed few layer graphene
Energy Technology Data Exchange (ETDEWEB)
Mitra, Sreemanta [MLS Professor of Physics' Unit, Indian Association for the Cultivation of Science, Kolkata-700032 (India); Department of Physics, University of Calcutta, Kolkata-700009 (India); Mondal, Oindrila [Department of Physics, M.U.C. Woman' s College, Burdwan (India); Banerjee, Sourish [Department of Physics, University of Calcutta, Kolkata-700009 (India); Chakravorty, Dipankar [MLS Professor of Physics' Unit, Indian Association for the Cultivation of Science, Kolkata-700032 (India)
2013-01-14
Nickel-adsorbed graphene was prepared by first synthesizing graphite oxide (GO) by modified Hummers' method and then reducing a solution containing both GO and Ni{sup 2+}. Energy dispersive X-ray spectroscopy analysis showed 31 at. % nickel was present. Magnetization measurements under both dc and ac magnetic fields were carried out in the temperature range 2 K to 300 K. The zero field cooled and field cooled magnetization data showed a pronounced irreversibility at a temperature around 20 K. The analysis of the ac susceptibility data was carried out by both Vogel-Fulcher as well as power law. From dynamic scaling analysis, the microscopic flipping time {tau}{sub 0}{approx}10{sup -13}s and critical exponent z{nu}=5.9{+-}0.1 were found, indicating the presence of conventional spin glass in the system. The spin glass transition temperature was estimated as 19.5 K. Decay of thermoremanent magnetization was explained by stretched exponential function with a value of the exponent as 0.6. From the results, it is concluded that nickel adsorbed graphene behaves like a spin-glass.
Observation of spin-glass behavior in nickel adsorbed few layer graphene
International Nuclear Information System (INIS)
Mitra, Sreemanta; Mondal, Oindrila; Banerjee, Sourish; Chakravorty, Dipankar
2013-01-01
Nickel-adsorbed graphene was prepared by first synthesizing graphite oxide (GO) by modified Hummers' method and then reducing a solution containing both GO and Ni 2+ . Energy dispersive X-ray spectroscopy analysis showed 31 at. % nickel was present. Magnetization measurements under both dc and ac magnetic fields were carried out in the temperature range 2 K to 300 K. The zero field cooled and field cooled magnetization data showed a pronounced irreversibility at a temperature around 20 K. The analysis of the ac susceptibility data was carried out by both Vogel-Fulcher as well as power law. From dynamic scaling analysis, the microscopic flipping time τ 0 ∼10 −13 s and critical exponent zν=5.9±0.1 were found, indicating the presence of conventional spin glass in the system. The spin glass transition temperature was estimated as 19.5 K. Decay of thermoremanent magnetization was explained by stretched exponential function with a value of the exponent as 0.6. From the results, it is concluded that nickel adsorbed graphene behaves like a spin-glass.
Mean field games for cognitive radio networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2012-01-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
Weakly coupled mean-field game systems
Gomes, Diogo A.; Patrizi, Stefania
2016-01-01
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.
Mean-field games for marriage.
Directory of Open Access Journals (Sweden)
Dario Bauso
Full Text Available This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
Mean Field Games with a Dominating Player
Energy Technology Data Exchange (ETDEWEB)
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Relativistic Chiral Mean Field Model for Finite Nuclei
Ogawa, Y.; Toki, H.; Tamenaga, S.; Haga, A.
2009-08-01
We present a relativistic chiral mean field (RCMF) model, which is a method for the proper treatment of pion-exchange interaction in the nuclear many-body problem. There the dominant term of the pionic correlation is expressed in two-particle two-hole (2p-2h) states with particle-holes having pionic quantum number, J^{π}. The charge-and-parity-projected relativistic mean field (CPPRMF) model developed so far treats surface properties of pionic correlation in 2p-2h states with J^{π} = 0^{-} (spherical ansatz). We extend the CPPRMF model by taking 2p-2h states with higher spin quantum numbers, J^{π} = 1^{+}, 2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He nucleus as a pilot calculation for the study of medium and heavy nuclei. We study the behavior of energy convergence with the pionic quantum number, J^{π}, and find convergence around J^{π}_{max} = 6^{-}. We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. The energy contribution of about 50% of the net two-body interaction comes from the tensor part and 20% comes from the spin-spin central part of the pion-exchange interaction.}
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Mean-field models and superheavy elements
International Nuclear Information System (INIS)
Reinhard, P.G.; Bender, M.; Maruhn, J.A.; Frankfurt Univ.
2001-03-01
We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations. (orig.)
Obstacle mean-field game problem
Gomes, Diogo A.; Patrizi, Stefania
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Das, Santanu; Choudhary, Kamal; Chernatynskiy, Aleksandr; Choi Yim, Haein; Bandyopadhyay, Asis K.; Mukherjee, Sundeep
2016-06-01
High-performance magnetic materials have immense industrial and scientific importance in wide-ranging electronic, electromechanical, and medical device technologies. Metallic glasses with a fully amorphous structure are particularly suited for advanced soft-magnetic applications. However, fundamental scientific understanding is lacking for the spin-exchange interaction between metal and metalloid atoms, which typically constitute a metallic glass. Using an integrated experimental and molecular dynamics approach, we demonstrate the mechanism of electron interaction between transition metals and metalloids. Spin-exchange interactions were investigated for a Fe-Co metallic glass system of composition [(Co1-x Fe x )0.75B0.2Si0.05]96Cr4. The saturation magnetization increased with higher Fe concentration, but the trend significantly deviated from simple rule of mixtures. Ab initio molecular dynamics simulation was used to identify the ferromagnetic/anti-ferromagnetic interaction between the transition metals and metalloids. The overlapping band-structure and density of states represent ‘Stoner type’ magnetization for the amorphous alloys in contrast to ‘Heisenberg type’ in crystalline iron. The enhancement of magnetization by increasing iron was attributed to the interaction between Fe 3d and B 2p bands, which was further validated by valence-band study.
Probing quantum spin glass like system with a double quantum dot
Koh, C. Y.; Kwek, L. C.
2016-06-01
We study the ground state properties of a 4-qubit spin glass like (SGL) chain with probes at the end of the chain and compare our results with the non-spin glass like (NSGL) case. The SGL is modeled as a spin chain with nearest-neighbor couplings, taking on normal variates with mean J and variance Δ2. The entanglement between the probes is used to detect any discontinuity in the ground state energy spectrum. For the NSGL case, it was found that the concurrence of the probes exhibits sharp transitions whenever there are abrupt changes in the energy spectrum. In particular, for the 4-qubit case, there is a sudden change in the ground state energy at an external magnetic field B of around 0.66 (resulting in a drop in concurrence of the probes) and 1.7 (manifest as a spike). The latter spike persists for finite temperature case. For the SGL sample with sufficiently large Δ, however, the spike is absent. Thus, an absence in the spike could act as a possible signature of the presence of SGL effects. Moreover, the sudden drop in concurrence at B ≈ 0.66 does not disappear but gets smeared with increasing Δ. However, this drop can be accentuated with a smaller probe coupling. The finite temperature case is also briefly discussed.
A regularized stationary mean-field game
Yang, Xianjin
2016-01-01
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Mean-field theory and solitonic matter
International Nuclear Information System (INIS)
Cohen, T.D.
1989-01-01
Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
Mean-field Ensemble Kalman Filter
Law, Kody; Tembine, Hamidou; Tempone, Raul
2015-01-01
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature
Mean Field Type Control with Congestion
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)
2016-06-15
We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
Configuration mixing of mean-field states
International Nuclear Information System (INIS)
Bender, M; Heenen, P-H
2005-01-01
Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes
International Nuclear Information System (INIS)
Al-Jalali, Muhammad A.; Kayali, Fawaz A.
2000-01-01
Full text.The spin glass of: (Cu-Mn, Ag-Mn, Au-Mn, Au-Fe) alloys has been extensively studied. The availability of published and assured experimental data on the susceptibility x(T) of this alloys has enabled the design and application of phenomenological approach to the spin glass state of these interesting alloys. The use of and advanced (S.P.S.S) computer software has resulted revealing some important features of the spin glass in these alloys, the most important of which is that the spin glass state do not represent as phase change
Lisewski, Andreas Martin; Lichtarge, Olivier
2010-08-15
Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial risks. Here we show that investors can overcome this complexity and globally minimize risk in portfolio models for any given expected return, provided the relative margin requirement remains below a critical, empirically measurable value. In practice, for markets with centrally regulated margin requirements, a rational stabilization strategy would be keeping margins small enough. This result follows from ground states of the random field spin glass Ising model that can be calculated exactly through convex optimization when relative spin coupling is limited by the norm of the network's Laplacian matrix. In that regime, this novel approach is robust to noise in empirical data and may be also broadly relevant to complex networks with frustrated interactions that are studied throughout scientific fields.
International Nuclear Information System (INIS)
Magalhaes, S.G.; Zimmer, F.M.; Kipper, C.J.; Calegari, E.J.
2007-01-01
The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising SG model with a local BCS pairing interaction in the presence of a transverse magnetic field Γ. The spins in different sublattices interact with Gaussian random couplings with an antiferromagnetic mean. The problem is formulated in a Grassmann path integral formalism. The static ansatz and the replica symmetry are used to obtain the half-filling thermodynamic potential. The results are shown in phase diagrams that exhibit a complex transition line separating the PAIR phase from the others. This line is second order at high temperature which ends in a tricritical point. The presence of Γ affects deeply the transition lines
International Nuclear Information System (INIS)
Mishra, Utkarsh; Rakshit, Debraj; Prabhu, R; Sen, Aditi; Sen, Ujjwal
2016-01-01
Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of a one-dimensional array of quantum spin-1/2 particles, governed by the Heisenberg spin glass Hamiltonian with natural or engineered quenched disordered couplings in an external magnetic field. These systems allow disorder-induced enhancement for bipartite and multipartite observables. Here we show that simultaneous application of independent quenched disorders results in disorder-induced enhancement, while the same is absent with individual application of the same disorders. We term the phenomenon as constructive interference and the corresponding parameter stretches as the Venus regions. Interestingly, it has only been observed for multiparty entanglement and is absent for the single- and two-party physical quantities. (paper)
Superconductivity and spin fluctuations in M-Zr metallic glasses (M = Cu, Ni, Co, and Fe)
International Nuclear Information System (INIS)
Altounian, Z.; Strom-Olsen, J.O.
1983-01-01
The superconducting transition temperature, upper critical field, and magnetic susceptibility have been measured in four binary metallic glass systems: Cu-Zr, Ni-Zr, Co-Zr, and Fe-Zr. For each alloy system, a full and continuous range of Zr-rich compositions accessible by melt spinning has been examined. For Cu-Zr, the range is 0.75>x>0.30; for Ni-Zr, 0.80>x>0.30; for Co-Zr, 0.80>x>0.48, and for Fe-Zr, 0.80>x>0.55 (x being the concentration of Zr in at. %). The results show clearly the influence of spin fluctuations in reducing the superconducting transition temperature. The data have been successfully analyzed using a modified form of the McMillan equation together with expressions for the Stoner enhanced magnetic susceptibility and the Ginsburg-Landau-Abrikosov-Gor'kov expression for the upper critical field
Lisewski, Andreas Martin; Lichtarge, Olivier
2010-08-01
Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial risks. Here we show that investors can overcome this complexity and globally minimize risk in portfolio models for any given expected return, provided the margin requirement remains below a critical, empirically measurable value. In practice, for markets with centrally regulated margin requirements, a rational stabilization strategy would be keeping margins small enough. This result follows from ground states of the random field spin glass Ising model that can be calculated exactly through convex optimization when relative spin coupling is limited by the norm of the network’s Laplacian matrix. In that regime, this novel approach is robust to noise in empirical data and may be also broadly relevant to complex networks with frustrated interactions that are studied throughout scientific fields.
First-order phase transition in the quantum spin glass at T=0
Energy Technology Data Exchange (ETDEWEB)
Viana, J. Roberto; Nogueira, Yamilles; Sousa, J. Ricardo de
2003-05-26
The van Hemmen model with transverse and random longitudinal field is studied to analyze the tricritical behavior in the quantum Ising spin glass at T=0. The free energy and order parameter are calculated for two types of probability distributions: Gaussian and bimodal. We obtain the phase diagram in the {omega}-H plane, where {omega} and H are the transverse and random longitudinal fields, respectively. For the case of Gaussian distribution the phase transition is of second order, while the bimodal distribution we observe second-order transition for high-transverse field and first-order transition for small transverse field, with a tricritical point in the phase diagram.
First-order phase transition in the quantum spin glass at T=0
International Nuclear Information System (INIS)
Viana, J. Roberto; Nogueira, Yamilles; Sousa, J. Ricardo de
2003-01-01
The van Hemmen model with transverse and random longitudinal field is studied to analyze the tricritical behavior in the quantum Ising spin glass at T=0. The free energy and order parameter are calculated for two types of probability distributions: Gaussian and bimodal. We obtain the phase diagram in the Ω-H plane, where Ω and H are the transverse and random longitudinal fields, respectively. For the case of Gaussian distribution the phase transition is of second order, while the bimodal distribution we observe second-order transition for high-transverse field and first-order transition for small transverse field, with a tricritical point in the phase diagram
Comparison of high-field Moessbauer and μSR investigations on spin glasses
International Nuclear Information System (INIS)
Bogner, J.; Reissner, M.; Steiner, W.; Cywinski, R.; Dann, J.A.; Telling, M.T.F.
2001-01-01
We report on the analysis of μSR and Moessbauer measurements of the metallic spin glasses Y(Fe 0.65 Al 0.35 ) 2 and Y(Fe 0.4 Al 0.6 ) 2 above the freezing temperature (T f ) in terms of a model taking into account a dynamical process of stochastic formation and decay of magnetically correlated regions. By this model a comparison of the autocorrelation function determined by the two different measuring techniques is possible. For the temperature dependence of the autocorrelation time we find fair agreement between both experiments for T>2T f
Search for the Heisenberg spin glass on rewired cubic lattices with antiferromagnetic interaction
International Nuclear Information System (INIS)
Surungan, Tasrief
2016-01-01
Spin glass (SG) is a typical magnetic system which is mainly characterized by a frozen random spin orientation at low temperatures. Frustration and randomness are considered to be the key ingredients for the existence of SGs. Previously, Bartolozzi et al . [Phys. Rev. B73, 224419 (2006)] found that the antiferromagnetic (AF) Ising spins on scale free network (SFN) exhibited SG behavior. This is purely AF system, a new type of SG different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely due to a topological factor and its randomness is brought by irregular connectivity. Recently, it was reported that the AF Heisenberg model on SFN exhibited SG behavior [Surungan et al ., JPCS, 640, 012005 (2015)/doi:10.1088/1742-6596/640/1/012005]. In order to accommodate the notion of spatial dimension, we further investigated this type of system by studying an AF Heisenberg model on rewired cubic lattices, constructed by adding one extra bond randomly connecting each spin to one of its next-nearest neighbors. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase. (paper)
Energy Technology Data Exchange (ETDEWEB)
Ma, Ji; Chen, Kezheng, E-mail: kchen@qust.edu.cn
2016-05-15
In this study, room-temperature spin-glass behaviors were observed in flake-like oriented attached hematite (α-Fe{sub 2}O{sub 3}) and iron phosphate hydroxide hydrate (Fe{sub 5}(PO{sub 4}){sub 4}(OH){sub 3}·2H{sub 2}O) single crystals. Remarkably, their coercivity (H{sub C}) values were found to be almost invariable at various given temperatures from 5 to 300 K. The spin topographic map in these flakes was assumed as superparamagnetic (SPM) “islands” isolated by spin glass (SG)-like “bridges”. A spin-glass model was then proposed to demonstrate the spin frustration within these “bridges”, which were formed by the staggered atomic planes in the uneven surfaces belonging to different attached nanoparticles. Under the spatial limitation and coupling shield of these “bridges”, the SPM “islands” were found to be collectively frozen to form a superspin glass (SSG) state below 80 K in weak applied magnetic fields; whereas, when strong magnetic fields were applied, the magnetic coupling of these “islands” would become superferromagnetic (SFM) through tunneling superexchange, so that, these SFM spins could antiferromagnetically couple with the SG-like “bridges” to yield pronounced exchange bias (EB) effect. - Highlights: • Room-temperature spin-glass state was found in 2D oriented attached single crystals. • Coercivity values were found to be almost invariable at different temperatures. • The spin topographic map was assumed as SPM “islands” isolated by SG-like “bridges”.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*
Directory of Open Access Journals (Sweden)
Kostyantyn Kechedzhi
2016-05-01
Full Text Available Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
One-loop topological expansion for spin glasses in the large connectivity limit
Chiara Angelini, Maria; Parisi, Giorgio; Ricci-Tersenghi, Federico
2018-01-01
We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with a field in the high connectivity limit, following the methodological scheme proposed in a recent work. The results are completely equivalent to the well-known ones, found by standard field-theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple physical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin-glass phase. Sharing with finite-dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.
Formation and partial melting of two types of spin-cluster glass behavior in vanadate spinel
International Nuclear Information System (INIS)
Huang Yuanjie; Pi Li; Tan Shun; Zhang Yuheng; Yang Zhaorong
2012-01-01
We report the doping effect on the various properties of spinels Co 1-x Zn x V 2 O 4 (0 ≤ x ≤ 0.2). For the parent compounds, the rise in magnetization, the valley in thermal conductance, the transition from the ferromagnetic arrangement to non-collinear alignment indicated by the specific heat for the V sublattice, especially the frequency dependence of AC susceptibility around T 1 = 59 K, verify the occurrence of the transition at T 1 besides the ferrimagnetic transition at T C . The ferrimagnetic transition at T C induces the spin-cluster glass behavior and the transition at T 1 yields the new spin-cluster glass (NSCG) behavior. As the Zn 2+ -doped content increases, the above phenomena are gradually weakening to vanishing, but the glassy behavior at T C still exists for all samples. Through the fourth-order perturbation theory, we discuss the reasons for the gradual vanishing of the transition at T 1 . (paper)
Elementary excitations and the phase transition in the bimodal Ising spin glass model
International Nuclear Information System (INIS)
Jinuntuya, N; Poulter, J
2012-01-01
We show how the nature of the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference L. This 2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet. The spatial influence of the frustration must be limited and not wrap around the system if L is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating the magnetization or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass state occurs. The value p c = 0.1045(11) is in reasonable agreement with the literature
Comparison of silicone and spin-on glass packaging materials for light-emitting diode encapsulation
Energy Technology Data Exchange (ETDEWEB)
Chang, Liann-Be; Pan, Ke-Wei; Yen, Chia-Yi [Department of Electronic Engineering and Green Technology Research Center, Chang Gung University, Taoyuan, Taiwan (China); Jeng, Ming-Jer, E-mail: mjjeng@mail.cgu.edu.tw [Department of Electronic Engineering and Green Technology Research Center, Chang Gung University, Taoyuan, Taiwan (China); Wu, Chun-Te; Hu, Sung-Cheng; Kuo, Yang-Kuao [Chemical Systems Research Division, Chung-Shan Institute of Science and Technology Armaments Bureau, MND, Taoyuan, Taiwan (China)
2014-11-03
Traditional white light light-emitting diode (LED) encapsulation is performed by mixed phosphors and silicone coating on LED die. However, this encapsulation with silicone coating incurs overheated temperatures and yellowing problem. Therefore, this work attempts to replace silicone paste by using spin-on-glass (SOG) materials. Experimental results indicate that although initial brightness of SOG-based packaging is lower than that of silicone packaging, its light attenuation is significantly lower than that of silicone for a long lighting time. After the LED power is turned on for 12 h, the brightness of LED with silicone and SOG material packaging decreases from 84 to 48 lm and 73 to 59 lm, respectively. Therefore, SOG material provides an alternative packaging solution for high power LED lighting applications. - Highlights: • Spin-on-glass (SOG) material was used to replace silicone coating for LED packaging. • Initial brightness of SOG packaging is lower than that of silicone packaging. • Over time, light attenuation in SOG is much lower than that in silicone. • Color rendering index and brightness of LED packaging was optimized by Taguchi method.
Coexistence of ferromagnetism and spin glass behavior in antiferromagnetic Y2BaCuO5
International Nuclear Information System (INIS)
Zhu, Zhonghua; Gao, Daqiang; Zhang, Jing; Shi, Zhenhua; Gao, Hua; Yang, Zhaolong; Zhang, Zhipeng; Xue, Desheng
2013-01-01
Highlights: • Room temperature ferromagnetism is observed in ultrafine Y 2 BaCuO 5 particles. • The observed ferromagnetism originates from the oxygen defects. • A very interesting spin glass transition located at about 110 K is found. -- Abstract: We report the synthesis of a series of Y 2 BaCuO 5 samples by varying the annealing temperature with a citrate pyrolysis technique. X-ray diffraction patterns, scanning electron microscopy and transmission electron microscopy observation show the formation of a columnar Y 2 BaCuO 5 phase and these samples are composed of many irregular particles with different particle size. Magnetic measurements show that these samples exhibit room temperature ferromagnetism and the saturation magnetization decreases with increasing sintering temperature. Post-heating treatment under argon atmosphere can enhance the ferromagnetism greatly, suggesting that the magnetism is attributed to the surface oxygen defects. By measuring magnetization versus temperature curves after zero field cooling with various applied magnetic fields, two magnetic phase transitions located at about 11 and 110 K are revealed. The position of the peak at about 11 K is independent of the magnetic field; the other peak, however, becomes rounder and shifts to lower temperatures with increasing the magnetic field, showing a strong field dependence. In addition, the virgin magnetization curves with the measured temperature below 110 K display an S-type. These features are suggestive of an antiferromagnetic phase transition at about 11 K and a spin glass transition at about 110 K
Antiferromagnetic and topological states in silicene: A mean field study
Liu, Feng; Liu, Cheng-Cheng; Yao, Yu-Gui
2015-08-01
It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K‧ for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state. Project supported by the National Key Basic Research Program of China (Grant Nos. 2014CB920903, 2013CB921903, 2011CBA00108, and 2012CB937500), the National Natural Science Foundation of China (Grant Nos. 11021262, 11172303, 11404022, 11225418, and 11174337), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121101110046), the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Grant No. 2014CX04028), and the Basic Research Funds of Beijing Institute of Technology (Grant No. 20141842001).
Moore, M A; Katzgraber, Helmut G
2014-10-01
Starting from preferences on N proposed policies obtained via questionnaires from a sample of the electorate, an Ising spin-glass model in a field can be constructed from which a political party could find the subset of the proposed policies which would maximize its appeal, form a coherent choice in the eyes of the electorate, and have maximum overlap with the party's existing policies. We illustrate the application of the procedure by simulations of a spin glass in a random field on scale-free networks.
Electron spin resonance studies of iron-group impurities in beryllium fluoride glasses
Energy Technology Data Exchange (ETDEWEB)
Griscom, D L; Stapelbroek, M [Naval Research Lab., Washington, DC (USA); Weber, M J [California Univ., Livermore (USA). Lawrence Livermore National Lab.
1980-11-01
Electron spin resonance investigations have been carried out on unirradiated BeF/sub 2/ glasses. Two relatively intense resonances were observed in a water-free distilled glass known to contain 49 ppM Ni, 13 ppM Mn, and < 20 ppM Fe. One of these was the paramagnetic resonance spectrum of Mn/sup 2 +/. Analysis of the observed /sup 19/F superhyperfine structure demonstrated this manganese to occupy distorted octahedral sites in the glass network. The second resonance was shown by temperature and frequency dependence studies, coupled with computer line shape analysis, to be a ferromagnetic resonance signal due to precipitated ferrite phases. The data suggest that these ferrites are somewhat heterogeneous and most likely comprize magnetite-like phases similar to NiFe/sub 2/O/sub 4/. An optical extinction curve rising into the ultraviolet with an approximate lambda/sup -4/ dependence is tentatively ascribed to light scattering by ferrite particles approximately 1000 Angstroems in diameter.
Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction
Energy Technology Data Exchange (ETDEWEB)
Surungan, Tasrief, E-mail: tasrief@unhas.ac.id; Bansawang, B.J.; Tahir, Dahlang [Department of Physics, Hasanuddin University, Makassar, South Sulawesi 90245 (Indonesia)
2016-03-11
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.
Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction
International Nuclear Information System (INIS)
Surungan, Tasrief; Bansawang, B.J.; Tahir, Dahlang
2016-01-01
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Low-temperature spin dynamics of a valence bond glass in Ba2YMoO6
International Nuclear Information System (INIS)
De Vries, M A; Piatek, J O; Rønnow, H M; Misek, M; Lord, J S; Bos, J-W G
2013-01-01
We carried out ac magnetic susceptibility measurements and muon spin relaxation spectroscopy on the cubic double perovskite Ba 2 YMoO 6 , down to 50 mK. Below ∼1 K the muon relaxation is typical of a magnetic insulator with a spin-liquid type ground state, i.e. without broken symmetries or frozen moments. However, the ac susceptibility revealed a dilute-spin-glass-like transition below ∼1 K. Antiferromagnetically coupled Mo 5+ 4d 1 electrons in triply degenerate t 2g orbitals are in this material arranged in a geometrically frustrated fcc lattice. Bulk magnetic susceptibility data has previously been interpreted in terms of a freezing to a heterogeneous state with non-magnetic sites where 4d 1 electrons have paired in spin-singlets dimers, and residual unpaired Mo 5+ 4d 1 electron spins. Based on the magnetic heat capacity data it has been suggested that this heterogeneity is the result of kinetic constraints intrinsic to the physics of the pure system (possibly due to topological overprotection) leading to a self-induced glass of valence bonds between neighbouring 4d 1 electrons. The muon spin relaxation (μSR) unambiguously points to a heterogeneous state with a static arrangement of unpaired electrons in a background of (valence bond) dimers between the majority of Mo 5+ 4d electrons. The ac susceptibility data indicate that the residual magnetic moments freeze into a dilute-spin-glass-like state. This is in apparent contradiction with the muon-spin decoupling at 50 mK in fields up to 200 mT, which indicates that, remarkably, the time scale of the field fluctuations from the residual moments is ∼5 ns. Comparable behaviour has been observed in other geometrically frustrated magnets with spin-liquid-like behaviour and the implications of our observations on Ba 2 YMoO 6 are discussed in this context. (paper)
Low-temperature spin dynamics of a valence bond glass in Ba2YMoO6
de Vries, M. A.; Piatek, J. O.; Misek, M.; Lord, J. S.; Rønnow, H. M.; Bos, J.-W. G.
2013-04-01
We carried out ac magnetic susceptibility measurements and muon spin relaxation spectroscopy on the cubic double perovskite Ba2YMoO6, down to 50 mK. Below ∼1 K the muon relaxation is typical of a magnetic insulator with a spin-liquid type ground state, i.e. without broken symmetries or frozen moments. However, the ac susceptibility revealed a dilute-spin-glass-like transition below ∼1 K. Antiferromagnetically coupled Mo5+ 4d1 electrons in triply degenerate t2g orbitals are in this material arranged in a geometrically frustrated fcc lattice. Bulk magnetic susceptibility data has previously been interpreted in terms of a freezing to a heterogeneous state with non-magnetic sites where 4d1 electrons have paired in spin-singlets dimers, and residual unpaired Mo5+ 4d1 electron spins. Based on the magnetic heat capacity data it has been suggested that this heterogeneity is the result of kinetic constraints intrinsic to the physics of the pure system (possibly due to topological overprotection) leading to a self-induced glass of valence bonds between neighbouring 4d1 electrons. The muon spin relaxation (μSR) unambiguously points to a heterogeneous state with a static arrangement of unpaired electrons in a background of (valence bond) dimers between the majority of Mo5+ 4d electrons. The ac susceptibility data indicate that the residual magnetic moments freeze into a dilute-spin-glass-like state. This is in apparent contradiction with the muon-spin decoupling at 50 mK in fields up to 200 mT, which indicates that, remarkably, the time scale of the field fluctuations from the residual moments is ∼5 ns. Comparable behaviour has been observed in other geometrically frustrated magnets with spin-liquid-like behaviour and the implications of our observations on Ba2YMoO6 are discussed in this context.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Spin-glass behavior in the S=1/2 fcc ordered perovskite Sr2CaReO6
International Nuclear Information System (INIS)
Wiebe, C.R.; Greedan, J.E.; Luke, G.M.; Gardner, J.S.
2002-01-01
The ordered perovskite Sr 2 CaReO 6 of monoclinic symmetry [space group P2 1 /n,a=5.7556(3) A,b=5.8534(3) A,c=8.1317(4) A,β=90.276(5) deg. at T=4 K] has been synthesized using standard solid-state chemistry techniques. The difference in the size and charge of the cations induces an ordering of the B site Ca 2+ and Re 6+ ions which leads to a distorted fcc lattice of spin-(1/2) Re 6+ (5d 1 ) moments. dc magnetic susceptibility measurements indicate a maximum at T G ∼14 K and an irreversibility in the field-cooled and zero-field-cooled data at ∼22 K that is believed to be caused by the geometric frustration inherent in the fcc structure. Neutron-scattering measurements confirm the absence of magnetic long-range order, and muon spin relaxation experiments indicate the presence of an abrupt spin freezing at T G . Specific heat measurements reveal a broad anomaly typical of spin glasses and no sharp feature. 65% of the spin entropy is released at low temperatures. The low-temperature data do not show the expected linear temperature dependence, but rather a T 3 relationship, as is observed, typically, for antiferromagnetic spin waves. The material is characterized as an unconventional, essentially disorder-free, spin glass
Superheavy nuclei: a relativistic mean field outlook
International Nuclear Information System (INIS)
Afanasjev, A.V.
2006-01-01
The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z = 120 and N = 172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z = 120 and N = 172. The shell gaps at Z = 126 and N = 184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin-Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP
Effective masses and the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Sartor, R.
1985-01-01
The effective mass characterizes the energy dependence of the empirical average nuclear potential. This energy dependence has two different sources, namely the nonlocality in space of the microscopic mean field on the one hand, and its true energy dependence on the other hand. Correspondingly it is convenient to divide the effective mass into two components, the k-mass and the ω-mass. The latter is responsible for the existence of a peak in the energy dependence of the effective mass. This peak is located near the Fermi energy in nuclear matter and in nuclei, as well as in the electron gas, the hard sphere Fermi gas and liquid helium 3. A related phenomenon is the existence of a low energy anomaly in the energy dependence of the optical model potential between two heavy ions. (orig.)
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Spin-on-glass coatings for the generation of super-polishedsubstrates for extreme ultraviolet optics
Energy Technology Data Exchange (ETDEWEB)
Salmassi, Farhad; Naulleau, Patrick P.; Gullikson, Eric M.
2005-01-01
Substrates intended for use as extreme ultraviolet (EUV) optics have extremely stringent requirements in terms of finish. These requirements can dramatically increase the cost and fabrication time, especially when non-conventional shapes, such as toroids, are required. Here we present a spin-on-glass resist process capable of generating super-polished parts from inexpensive substrates. The method has been used to render diamond-turned substrates compatible for use as EUV optics. Toroidal diamond-turned optics with starting rms roughness in the 3.3 to 3.7 nm range have been smoothed to the 0.4 to 0.6 nm range. EUV reflectometry characterization of these optics has demonstrated reflectivities of approximately 63%.
Study of dilution of Spin-On Glass by Fourier transform infrared spectroscopy
International Nuclear Information System (INIS)
Dominguez, Miguel; Rosales, Pedro; Torres, Alfonso; Moreno, Mario; Orduña, Abdu
2012-01-01
In this work, we study the dilution of Spin-On Glass (SOG) in order to obtain high quality SiO 2 films at 200 °C, with optical and electrical characteristics similar to those of the thermally grown SiO 2 . For the production of SiO 2 films we used 2-propanol and deionized water (DI) as diluents for the SOG and we compared the electrical and optical film properties with those of the films obtained from undiluted SOG. From Fourier transform infrared spectroscopy we observed a considerable reduction of Si-OH (920 cm −1 ), O-H (3490 cm −1 ) and C-H, C-O bonds (1139 cm −1 ) in the films produced from SOG diluted with DI. Besides the above, the insulator breakdown field was approximately 21 MV/cm, the refractive index and the dielectric constant were close to those of the thermally grown SiO 2 . Our results suggest that the film produced from SOG diluted with DI and cured at 200 °C is an excellent candidate to be used as insulator on flexible and large-area electronics. - Highlights: ► Preparation of high quality silicon oxide (SiO 2 ) films at 200 °C. ► Dilution of Spin-On Glass (SOG) solution was studied. ► Dilution of SOG is necessary to obtain high quality films annealed at 200 °C. ► n and k are close to those of the thermally grown SiO 2 .
Study of dilution of Spin-On Glass by Fourier transform infrared spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Miguel, E-mail: mdominguez@inaoep.mx [National Institute for Astrophysics, Optics and Electronics (INAOE), Electronics Department, Luis Enrique Erro No. 1, Puebla 72840 (Mexico); Rosales, Pedro; Torres, Alfonso; Moreno, Mario [National Institute for Astrophysics, Optics and Electronics (INAOE), Electronics Department, Luis Enrique Erro No. 1, Puebla 72840 (Mexico); Orduna, Abdu [CIBA-Tlaxcala, Instituto Politecnico Nacional, Tepetitla, Tlax. 90700 (Mexico)
2012-05-31
In this work, we study the dilution of Spin-On Glass (SOG) in order to obtain high quality SiO{sub 2} films at 200 Degree-Sign C, with optical and electrical characteristics similar to those of the thermally grown SiO{sub 2}. For the production of SiO{sub 2} films we used 2-propanol and deionized water (DI) as diluents for the SOG and we compared the electrical and optical film properties with those of the films obtained from undiluted SOG. From Fourier transform infrared spectroscopy we observed a considerable reduction of Si-OH (920 cm{sup -1}), O-H (3490 cm{sup -1}) and C-H, C-O bonds (1139 cm{sup -1}) in the films produced from SOG diluted with DI. Besides the above, the insulator breakdown field was approximately 21 MV/cm, the refractive index and the dielectric constant were close to those of the thermally grown SiO{sub 2}. Our results suggest that the film produced from SOG diluted with DI and cured at 200 Degree-Sign C is an excellent candidate to be used as insulator on flexible and large-area electronics. - Highlights: Black-Right-Pointing-Pointer Preparation of high quality silicon oxide (SiO{sub 2}) films at 200 Degree-Sign C. Black-Right-Pointing-Pointer Dilution of Spin-On Glass (SOG) solution was studied. Black-Right-Pointing-Pointer Dilution of SOG is necessary to obtain high quality films annealed at 200 Degree-Sign C. Black-Right-Pointing-Pointer n and k are close to those of the thermally grown SiO{sub 2}.
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
Non-local correlations within dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Non-local correlations within dynamical mean field theory
International Nuclear Information System (INIS)
Li, Gang
2009-03-01
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly*
Directory of Open Access Journals (Sweden)
Helmut G. Katzgraber
2015-09-01
Full Text Available There has been considerable progress in the design and construction of quantum annealing devices. However, a conclusive detection of quantum speedup over traditional silicon-based machines remains elusive, despite multiple careful studies. In this work we outline strategies to design hard tunable benchmark instances based on insights from the study of spin glasses—the archetypal random benchmark problem for novel algorithms and optimization devices. We propose to complement head-to-head scaling studies that compare quantum annealing machines to state-of-the-art classical codes with an approach that compares the performance of different algorithms and/or computing architectures on different classes of computationally hard tunable spin-glass instances. The advantage of such an approach lies in having to compare only the performance hit felt by a given algorithm and/or architecture when the instance complexity is increased. Furthermore, we propose a methodology that might not directly translate into the detection of quantum speedup but might elucidate whether quantum annealing has a “quantum advantage” over corresponding classical algorithms, such as simulated annealing. Our results on a 496-qubit D-Wave Two quantum annealing device are compared to recently used state-of-the-art thermal simulated annealing codes.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-03
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Nonequilibrium dynamical mean-field theory
International Nuclear Information System (INIS)
Eckstein, Martin
2009-01-01
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Instabilities constraint and relativistic mean field parametrization
International Nuclear Information System (INIS)
Sulaksono, A.; Kasmudin; Buervenich, T.J.; Reinhard, P.-G.; Maruhn, J.A.
2011-01-01
Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria 20 determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors. (author)
Mean-field approach to unconventional superconductivity
International Nuclear Information System (INIS)
Sacks, William; Mauger, Alain; Noat, Yves
2014-01-01
Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody; Tembine, Hamidou; Tempone, Raul
2016-01-01
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Energy Technology Data Exchange (ETDEWEB)
Kumar, Ashwani; Sanger, Amit; Singh, Amit Kumar; Kumar, Arvind [Nanoscience Laboratory, Institute Instrumentation Centre, Indian Institute of Technology Roorkee, Roorkee 247667 (India); Kumar, Mohit [Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Chandra, Ramesh [Nanoscience Laboratory, Institute Instrumentation Centre, Indian Institute of Technology Roorkee, Roorkee 247667 (India)
2017-07-01
Highlights: • We have synthesized the α-MnO{sub 2} nanorods by using DC reactive sputtering. • We observed Spin glass and exchange bias behavior at low temperature in sputtered grown α-MnO{sub 2} nanorods. • Exchange bias arises due to exchange coupling of uncompensated FM spins and AFM spins at FM/AFM interface. - Abstract: Here, we present a single-step process to synthesize the α-MnO{sub 2} nanorods forest using reactive DC magnetron sputtering for the application of magnetic memories. The structural and morphological properties of the α-MnO{sub 2} nanorods were systematically studied using numerous analytical techniques, including X-ray diffraction, Raman spectroscopy, field-emission scanning electron microscopy and transmission electron microscopy. The magnetic measurements suggest that the α-MnO{sub 2} nanorods exhibit spin glass and exchange bias behaviour at low temperature. Such low temperature behaviour is explained by the core-shell type structure of nanorods. Antiferromagnetic core and shell of uncompensated ferromagnetic spins leads to the formation of antiferromagnetic/ferromagnetic (AFM/FM) interfaces, which originates exchange bias in the sample.
International Nuclear Information System (INIS)
Amjad, Jafar Mostafavi; Khalesifard, Hamid Reza; Slussarenko, Sergei; Karimi, Ebrahim; Santamato, Enrico; Marrucci, Lorenzo
2011-01-01
Samples of Ag + /Na + ion-exchanged glass that have been subject to intense laser irradiation may develop novel optical properties, as a consequence of the formation of patterns of silver nanoparticles and other structures. Here, we report the observation of a laser-induced permanent transverse birefringence, with the optical axis forming a radial pattern, as revealed by the spin-to-orbital angular momentum conversion occurring in a probe light beam. The birefringence pattern can be modeled well as resulting from thermally-induced stresses arising in the silver-doped glass during laser exposure, although the actual mechanism leading to the permanent anisotropy is probably more complex.
Field-induced cluster spin glass and inverse symmetry breaking enhanced by frustration
Schmidt, M.; Zimmer, F. M.; Magalhaes, S. G.
2018-03-01
We consider a cluster disordered model to study the interplay between short- and long-range interactions in geometrically frustrated spin systems under an external magnetic field (h). In our approach, the intercluster long-range disorder (J) is analytically treated to get an effective cluster model that is computed exactly. The clusters follow a checkerboard lattice with first-neighbor (J1) and second-neighbor (J2) interactions. We find a reentrant transition from the cluster spin-glass (CSG) state to a paramagnetic (PM) phase as the temperature decreases for a certain range of h. This inverse symmetry breaking (ISB) appears as a consequence of both quenched disorder with frustration and h, that introduce a CSG state with higher entropy than the polarized PM phase. The competitive scenario introduced by antiferromagnetic (AF) short-range interactions increases the CSG state entropy, leading to continuous ISB transitions and enhancing the ISB regions, mainly in the geometrically frustrated case (J1 =J2). Remarkably, when strong AF intracluster couplings are present, field-induced CSG phases can be found. These CSG regions are strongly related to the magnetization plateaus observed in this cluster disordered system. In fact, it is found that each field-induced magnetization jump brings a CSG region. We notice that geometrical frustration, as well as cluster size, play an important role in the magnetization plateaus and, therefore, are also relevant in the field-induced glassy states. Our findings suggest that competing interactions support ISB and field-induced CSG phases in disordered cluster systems under an external magnetic field.
Spin glass behavior in nanogranular La0.25Ca0.75MnO3 manganites
International Nuclear Information System (INIS)
2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" data-affiliation=" (Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" >Fernández-Martínez, Antoni; 2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" data-affiliation=" (Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" >García-Santiago, Antoni; 2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" data-affiliation=" (Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain))" >Hernàndez, Joan Manel; Zhang, Tao
2014-01-01
The magnetic properties of two nanogranular La 0.25 Ca 0.75 MnO 3 manganites with different average grain sizes have been studied. Besides the well-known exchange bias effect and the appearance of ferromagnetic clusters in the grains of both samples, the results show the occurrence of an antiferromagnetic transition and spin-glass properties. Both samples are described as core–shell magnetic systems, whose main difference is found in the interface between the outer ferromagnetic and the inner antiferromagnetic phases of the grains. - Highlights: • Nanogranular manganites show antiferromagnetism in magnetic measurements. • Exchange bias effect was observed in magnetic hysteresis cycles. • Spin-glass properties were detected at low temperatures. • A core-shell model was applied to describe the results in both samples. • These features have nothing to do with usual properties of nanoparticle manganites
Superconducting to spin-glass state transformation in β-pyrochlore KxOs2O6
Lee, C. C.; Lee, W. L.; Lin, J.-Y.; Tsuei, C. C.; Lin, J. G.; Chou, F. C.
2011-03-01
β-pyrochore KOs2O6, which shows superconductivity below ~9.7 K, has been converted into KxOs2O6 (x≲(2)/(3)-(1)/(2)) electrochemically to show spin-glass-like behavior below ~6.1 K. A room-temperature sample surface potential versus charge transfer scan indicates that there are at least two two-phase regions for x between 1 and 0.5. A rattling model of superconductivity for the title compound has been examined using electrochemical potassium de-intercalation. The significant reduction of superconducting volume fraction due to minor potassium reduction suggests the importance of defect and phase coherence in the rattling model. Magnetic susceptibility, resistivity, and specific heat measurement results have been compared between the superconducting and spin-glass-like samples.
International Nuclear Information System (INIS)
Hamed Hassani, S; Macris, Nicolas; Urbanke, Ruediger
2012-01-01
We consider a collection of Curie–Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite-range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error-correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behavior. We are interested in the van der Waals curve in a regime where the size of each Curie–Weiss model tends to infinity, and the length of the chain and range of the Kac interaction are large but finite. Below the critical temperature, and with appropriate boundary conditions, there appears a series of equilibrium states representing kink-like interfaces between the two equilibrium states of the individual system. The van der Waals curve oscillates periodically around the Maxwell plateau. These oscillations have a period inversely proportional to the chain length and an amplitude exponentially small in the range of the interaction; in other words, the spinodal points of the chain model lie exponentially close to the phase transition threshold. The amplitude of the oscillations is closely related to a Peierls–Nabarro free energy barrier for the motion of the kink along the chain. Analogies to similar phenomena and their possible algorithmic significance for graphical models of interest in coding theory and theoretical computer science are pointed out
Spin-glass state in the mixed system (Co1-xFex)2(OH)3Cl on deformed pyrochlore lattice
International Nuclear Information System (INIS)
Fujihala, M.; Hagihala, M.; Zheng, X.G.; Kawae, T.
2009-01-01
Magnetic interactions in a new geometrically frustrated system (Co 1-x Fe x ) 2 (OH) 3 Cl are investigated using magnetic susceptibility and μSR study. While Co 2 (OH) 3 Cl is ferromagnetic and Fe 2 (OH) 3 Cl antiferromagnetic, the partially substituted series (Co 1-x Fe x ) 2 (OH) 3 Cl show spin-glass behaviours, wherein ferromagnetic interactions prevail for low Fe concentration and antiferromagnetic ones prevail for high Fe concentration. In special, analysis of the AC magnetic susceptibility and ZF-μ + SR for the x=0.5 sample suggest that CoFe(OH) 3 Cl has both features of chemically disordered random spin glass and geometrically frustrated spin glass. It is also the first spin-glass system for the newly found geometric frustration series M 2 (OH) 3 X.
Doping of ZnO nanowires using phosphorus diffusion from a spin-on doped glass source
International Nuclear Information System (INIS)
Bocheux, A.; Robin, I. C.; Bonaimé, J.; Hyot, B.; Feuillet, G.; Kolobov, A. V.; Fons, P.; Mitrofanov, K. V.; Tominaga, J.; Tamenori, Y.
2014-01-01
In this article, we report on ZnO nanowires that were phosphorus doped using a spin on dopant glass deposition and diffusion method. Photoluminescence measurements suggest that this process yields p-doped ZnO. The spatial location of P atoms was studied using x-ray near-edge absorption structure spectroscopy and it is concluded that the doping is amphoteric with P atoms located on both Zn and O sites
International Nuclear Information System (INIS)
Mookerjee, A.
1984-09-01
The problem of spin-glass to ferromagnetic transition with increasing concentration is then one of the familiar nearest neighbour percolation but on the background of IIC. In the regime p<=psub(c) at T=Tsub(g)(p), the IIC forms a fractal background on which ferromagnetic percolation takes place. The equivalent statement is that the mobility edge Jsub(c)(p) moves outwards as p increases and at a critical psub(c) coincides with the band edge Jsub(B). At and above these concentrations the mode with highest energy is extended and we have the familiar paramagnetic to ferromagnetic transition as temperature is lowered across Jsub(B)/ksub(B). The physical justification of this picture is not at all transparent as in the case of the cluster percolation ideas. To this date no reliable estimates of the behaviour of Jsub(c)(p) as a function of p, for a purely off diagonal random matrix J(R) have been made
Search for the non-canonical Ising spin glass on rewired square lattices
Surungan, Tasrief
2018-03-01
A spin glass (SG) of non-canonical type is a purely antiferromagnetic (AF) system, exemplified by the AF Ising model on a scale free network (SFN), studied by Bartolozzi et al. [ Phys. Rev. B73, 224419 (2006)]. Frustration in this new type of SG is rendered by topological factor and its randomness is caused by random connectivity. As an SFN corresponds to a large dimensional lattice, finding non-canonical SG in lattice with physical dimension is desireable. However, a regular lattice can not have random connectivity. In order to obtain lattices with random connection and preserving the notion of finite dimension, we costructed rewired lattices. We added some extra bonds randomly connecting each site of a regular lattice to its next-nearest neighbors. Very recently, Surungan et al., studied AF Heisenberg system on rewired square lattice and found no SG behavior [AIP Conf. Proc. 1719, 030006 (2016)]. Due to the importance of discrete symmetry for phase transition, here we study similar structure for the Ising model (Z 2 symmetry). We used Monte Carlo simulation with Replica Exchange algorithm. Two types of structures were studied, firstly, the rewired square lattices with one extra bonds added to each site, and secondly, two bonds added to each site. We calculated the Edwards-Anderson paremeter, the commonly used parameter in searching for SG phase. The non-canonical SG is clearly observed in the rewired square lattice with two extra bonds added.
Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network
International Nuclear Information System (INIS)
Surungan, Tasrief; Zen, Freddy P; Williams, Anthony G
2015-01-01
Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in d-dimensional regular lattices for (d ≤ 3). We can make an analogy for the connectivity density (m) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of m for the existence of SG behaviour, analogous to the lower critical dimension (d l ) for the canonical SG systems. Here we study system with m = 2, 3, 4 and 5. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of m and estimated its corersponding critical temperature. (paper)
PREFACE: ELC International Meeting on Inference, Computation, and Spin Glasses (ICSG2013)
Kabashima, Yoshiyuki; Hukushima, Koji; Inoue, Jun-ichi; Tanaka, Toshiyuki; Watanabe, Osamu
2013-12-01
The close relationship between probability-based inference and statistical mechanics of disordered systems has been noted for some time. This relationship has provided researchers with a theoretical foundation in various fields of information processing for analytical performance evaluation and construction of efficient algorithms based on message-passing or Monte Carlo sampling schemes. The ELC International Meeting on 'Inference, Computation, and Spin Glasses (ICSG2013)', was held in Sapporo 28-30 July 2013. The meeting was organized as a satellite meeting of STATPHYS25 in order to offer a forum where concerned researchers can assemble and exchange information on the latest results and newly established methodologies, and discuss future directions of the interdisciplinary studies between statistical mechanics and information sciences. Financial support from Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan 'Exploring the Limits of Computation (ELC)' is gratefully acknowledged. We are pleased to publish 23 papers contributed by invited speakers of ICSG2013 in this volume of Journal of Physics: Conference Series. We hope that this volume will promote further development of this highly vigorous interdisciplinary field between statistical mechanics and information/computer science. Editors and ICSG2013 Organizing Committee: Koji Hukushima Jun-ichi Inoue (Local Chair of ICSG2013) Yoshiyuki Kabashima (Editor-in-Chief) Toshiyuki Tanaka Osamu Watanabe (General Chair of ICSG2013)
Internal structure transition of spin-on glass by electron beam irradiation
International Nuclear Information System (INIS)
Araki, Makoto; Taniguchi, Jun; Sawada, Nobuo; Utsumi, Takayuki; Miyamoto, Iwao
2007-01-01
The effects of electron beam (EB) irradiation on spin-on glass (SOG) were investigated using thermal desorption spectroscopy. We were able to employ heat treatment as a 'development process', since we discovered that heat treatment breaks different bonds in SOG depending on whether it is applied before or after EB irradiation of SOG. In the case, when heat treatment was applied before EB irradiation of SOG, it was possible to break the Si-C bond at about 500 deg. C. In the case, when heat treatment was applied after EB irradiation of SOG, on the other hand, the -SiC bond could be broken at a lower temperature of about 400 deg. C. Using this difference between the two bond-breaking temperatures, it was possible to develop SOG using thermal desorption development (TDD). Moreover, the bond-breaking mechanisms revealed that the organic components in SOG play an important role in TDD. Hence, in order to determine the influence of organic components on TDD, the development characteristics of SOG samples with 10% and 15% organic contents were investigated
A method that reveals the multi-level ultrametric tree hidden in p -spin-glass-like systems
International Nuclear Information System (INIS)
Baviera, R; Virasoro, M A
2015-01-01
In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs–Boltzmann partition function gives the information necessary to understand the equilibrium behavior of the system as a function of the temperature but is not enough if we are interested in the more general aspects of the hypersurface: it does not give us, for instance, the different degrees of ruggedness at different scales. In the context of the replica symmetry breaking (RSB) approach we discuss here a rather simple extension that can provide a much more detailed picture. The attractiveness of the method relies on the fact that it is conceptually transparent and the additional calculations are rather straightforward. We think that this approach reveals an ultrametric organisation with many levels in models like p-spin glasses when we include saddle points. In this first paper we present detailed calculations for the spherical p-spin glass model where we discover that the corresponding decreasing Parisi function q(x) codes this hidden ultrametric organisation. (paper)
International Nuclear Information System (INIS)
Marinari, E.; Zuliani, F.; Parisi, G.; Ricci-Tersenghi, F.; Ruiz-Lorenzo, J.J.
2000-04-01
We discuss Replica Symmetry Breaking (RSB) in Spin Glasses. We present an update about the state of the matter, both from the analytical and from the numerical point of view. We put a particular attention in discussing the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss about what happens in finite dimensional, realistic spin glasses. Together with a detailed review of some of most important features, facts, data, phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field and the dynamical approach. We present new numerical results for the behavior of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example the determination of the phase transition point, the correlation functions, the window overlaps, the dynamical behavior of the system). (author)
Classification of networks of automata by dynamical mean field theory
International Nuclear Information System (INIS)
Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.
1990-01-01
Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Plonka, A; Kevan, L
1976-11-01
A differential ESR saturation study of allowed transitions and forbidden proton spin-flip satellite transitions for trapped hydrogen atoms in sulfuric acid glasses indicates that angular modulation dominates the spin-lattice relaxation mechanisms and suggests that the modulation arises from motion of the H atom.
Copper oxide thin films anchored on glass substrate by sol gel spin coating technique
Krishnaprabha, M.; Venu, M. Parvathy; Pattabi, Manjunatha
2018-05-01
Owing to the excellent optical, thermal, electrical and photocatalytic properties, copper oxide nanoparticles/films have found applications in optoelectronic devices like solar/photovoltaic cells, lithium ion batteries, gas sensors, catalysts, magnetic storage media etc. Copper oxide is a p-type semiconductor material having a band gap energy varying from 1.2 eV-2.1 eV. Syzygium Samarangense fruit extract was used as reducing agent to synthesize copper oxide nanostructures at room temperature from 10 mM copper sulphate pentahydrate solution. The synthesized nanostructures are deposited onto glass substrate by spin coating followed by annealing the film at 200 °C. Both the copper oxide colloid and films are characterized using UV-Vis spectroscopy, field emission scanning electron microscopy (FESEM) and energy dispersive spectroscopy (EDS) techniques. Presence of 2 peaks at 500 nm and a broad peak centered around 800 nm in the UV-Vis absorbance spectra of copper oxide colloid/films is indicative of the formation of anisotropic copper oxide nanostructures is confirmed by the FESEM images which showed the presence of triangular shaped and rod shaped particles. The rod shaped particles inside island like structures were found in unannealed films whereas the annealed films contained different shaped particles with reduced sizes. The elemental analysis using EDS spectra of copper oxide nanoparticles/films showed the presence of both copper and oxygen. Electrical properties of copper oxide nanoparticles are affected due to quantum size effect. The electrical studies carried out on both unannealed and annealed copper oxide films revealed an increase in resistivity with annealing of the films.
Non-equilibrium mean-field theories on scale-free networks
International Nuclear Information System (INIS)
Caccioli, Fabio; Dall'Asta, Luca
2009-01-01
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks
Spin glass transition in the rhombohedral LiNi1/3Mn1/3Co1/3O2
International Nuclear Information System (INIS)
Bie, Xiaofei; Yang, Xu; Han, Bing; Chen, Nan; Liu, Lina; Wei, Yingjin; Wang, Chunzhong; Chen, Hong; Du, Fei; Chen, Gang
2013-01-01
Highlights: •The Rietveld analysis of XRD data reveals a single phase with rhombohedral structure. •Dc susceptibility data suggest a spin glass behavior at low T in the 333 compound. •The ac susceptibility measurements have been observed in the typical SG system. •Three models have been employed to study the behavior of the spin glass state. •Both geometrical frustration and disorder play important role in the formation of SG. -- Abstract: Layered LiNi 1/3 Mn 1/3 Co 1/3 O 2 has been synthesized by co-precipitation method, and the magnetic properties were comprehensively studied by dc and ac susceptibilities. The dc magnetization curves show the irreversibility and spin freezing behavior at 109 K and 9 K. The evolution of real and imaginary part of ac susceptibility under different frequencies indicates a spin glass transition at low temperature. Three models (the Néel–Arrhenius law, the Vogel–Fulcher law, and the power law) have been employed to study the relaxation behavior of the spin glass state. Both frustration and disorder play important role in the formation of spin glass
Yasin, Sk. Mohammad; Srinivas, V.; Kasiviswanathan, S.; Vagadia, Megha; Nigam, A. K.
2018-04-01
In the present study magnetic and electrical transport properties of transition metal substituted Co-Ga alloys (near critical cobalt concentration) have been investigated. Analysis of temperature and field dependence of dc magnetization and ac susceptibility (ACS) data suggests an evidence of reentrant spin glass (RSG) phase in Co55.5TM3Ga41.5 (TM = Co, Cr, Fe, Cu). The magnetic transition temperatures (TC and Tf) are found to depend on the nature of TM element substitution with the exchange coupling strength Co-Fe > Co-Co > Co-Cu > Co-Cr. From magnetization dynamics precise transition temperatures for the glassy phases are estimated. It is found that characteristic relaxation times are higher than that of spin glasses with minimal spin-cluster formation. The RSG behavior has been further supported by the temperature dependence of magnetotransport studies. From the magnetic field and substitution effects it has been established that the magnetic and electrical transport properties are correlated in this system.
Spin-glass-like behaviour in IrSr2RECu2O8 (RE=Sm and Eu)
International Nuclear Information System (INIS)
Santos-Garcia, A.J. dos; Duijn, J. van; Alario-Franco, M.A.
2008-01-01
We report the results of magnetic and specific heat measurements on the 1212-type compounds IrSr 2 RECu 2 O 8 with RE=Sm and Eu, prepared by high-pressure and high-temperature synthesis. The magnetic susceptibility of these compounds shows a large difference in the temperature dependence of the magnetization measured under zero-field-cooled and field-cooled conditions below 87 and 71 K, respectively, and upon further cooling below ∼10 K substantial maxima are observed too. Further AC susceptibility measurements support a glassy behaviour in lower magnetic transitions whereas the specific heat measurements do not show the typical long-range ordering commonly displayed in ferro, ferri or antiferromagnetic transitions. Hysteresis loops suggest the presence of magnetic clusters in the otherwise paramagnetic zone, indicating that these compounds probably display a reentrant spin-glass transition. Results are presented and discussed. - Graphical abstract: IrSr 2 RECu 2 O 8 with RE=Sm and Eu were prepared by high-pressure and high-temperature synthesis. Both samples adopt a M-1212-type perovskite structure and a microdomain texturing of the long c-axis is observed by TEM. A very interesting magnetic behaviour is observed in these materials. A 'cluster by cluster freezing' model is proposed, instead of the classical individual spin freezing one to explain the spin-glass-like behaviour that seems to coexist with weak ferromagnetism in both compounds
International Nuclear Information System (INIS)
Monthus, Cécile
2015-01-01
For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco (1979 Phys. Rev. D 19 3173) is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent ν = 1. Recently, Miyazaki and Nishimori (2013 Phys. Rev. E 87 032154) have proposed to study the disordered quantum Ising model in dimensions d > 1 by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the inequivalence of directions of their approach, we propose here an alternative procedure where the d directions are treated on the same footing. For the pure model, this leads to the correlation length exponents ν ≃ 0.625 in d = 2 (to be compared with the 3D classical Ising model exponent ν ≃ 0.63) and ν ≃ 0.5018 (to be compared with the 4D classical Ising model mean-field exponent ν = 1/2). For the disordered model in dimension d = 2, either ferromagnetic or spin-glass, the numerical application of the renormalization rules to samples of linear size L = 4096 yields that the transition is governed by an Infinite Disorder Fixed Point, with the activated exponent ψ ≃ 0.65, the typical correlation exponent ν typ ≃ 0.44 and the finite-size correlation exponent ν FS ≃ 1.25. We discuss the similarities and differences with the Strong Disorder Renormalization results. (paper)
Shen, Ka
2018-04-01
We study magnon spectra at finite temperature in yttrium iron garnet using a tight-binding model with nearest-neighbor exchange interaction. The spin reduction due to thermal magnon excitation is taken into account via the mean field approximation to the local spin and is found to be different at two sets of iron atoms. The resulting temperature dependence of the spin wave gap shows good agreement with experiment. We find that only two magnon modes are relevant to the ferromagnetic resonance.
Singh, R. R. P.; Young, A. P.
2017-12-01
We discuss generation of series expansions for Ising spin glasses with a symmetric ±J (i.e., bimodal) distribution on d -dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problems, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field h , for which we obtain high temperature series expansions in variables tanh(J /T ) and tanh(h /T ) . The quantum problem is a T =0 study of the Ising spin glass in a transverse magnetic field hT for which we obtain a perturbation theory in powers of J /hT . These methods require (i) enumeration and counting of all connected clusters that can be embedded in the lattice up to some order n , and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order n and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the ±J bonds and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the T =0 quantum system. Details of the calculational methods are presented.
International Nuclear Information System (INIS)
Hennion, M.; Hennion, B.; Mirebeau, I.; Lequien, S.; Hippert, F.
1988-01-01
We report small angle (SANS) and inelastic neutron scattering in zero and applied field for a-FeMn, NiMn and AuFe at composition where both ferromagnetic and frustration characters occur. We discuss the field evolution of the transverse correlations which arise below T c . A study of the field sensitivity of the spin wave anomalies in a-FeMn is reported
Spin-Glass Transition and Giant Paramagnetism in Heavily Hole-Doped Bi2Sr2Co2Oy
Hsu, Hung Chang; Lee, Wei-Li; Lin, Jiunn-Yuan; Young, Ben-Li; Kung, Hsiang-Hsi; Huang, Jian; Chou, Fang Cheng
2014-02-01
Hole-doped single crystals of misfit-layered cobaltate Bi2-xPbxSr2-zCo2Oy (x = 0-0.61, y = 8.28-8.62, and z = 0.01-0.22) have been successfully grown using the optical floating-zone method. Heavier hole doping has been achieved through both Pb substitution in the Bi site and the more effective Sr vacancy formation. The Co4+ : Co3+ ratio can be raised significantly from its original ˜1 : 1 to 4.5 : 1, as confirmed by iodometric titration. A spin-glass transition temperature of Tg ˜ 70 K is confirmed by ac susceptibility measurement when the Co4+ : Co3+ ratio becomes higher than 2 : 1, presumably owing to the significantly increased probability of triangular geometrical frustration among antiferromagnetically coupled localized Co4+ spins.
International Nuclear Information System (INIS)
Zimmer, F.M.; Magalhaes, S.G.
2007-01-01
The one-step replica symmetry breaking is used to study the competition between spin glass (SG) and antiferromagnetic order (AF) in two-sublattice fermionic Ising SG models in the presence of a transverse Γ and a parallel H magnetic fields. Inter- and intra-sublattice exchange interactions following Gaussian distributions are considered. The problem is formulated in a Grassmann path integral formalism within the static ansatz. Results show that H favors the non-ergodic mixed phase (AF+SG) and it destroys the AF. The Γ suppresses the magnetic orders, and the intra-sublattice interaction can introduce a discontinuous phase transition
Correlated spin glass generated by structural disorder in the amorphous Dy6Fe74B20 alloy
Tejada, J.; Martinez, B.; Labarta, A.; Chudnovsky, E. M.
1991-10-01
Magnetic properties of the amorphous Dy-Fe-B alloy are studied in terms of the correlated-spin-glass approach of Chudnovsky et al.$-- Features predicted by the theory are clearly observed in the experiment. It is shown that the magnetization law may be presented in the form where it is determined by the dimensionless correlation function of structural disorder, C(y), only. The analysis of the magnetization curve allows one to distinguish between different models of disorder in amorphous solids. Experimental data on Dy-Fe-B are in favor of C=exp(-1/2y2).
Correlated spin glass generated by structural disorder in the amorphous Dy6Fe74B20 alloy
International Nuclear Information System (INIS)
Tejada, J.; Martinez, B.; Labarta, A.; Chudnovsky, E.M.
1991-01-01
Magnetic properties of the amorphous Dy-Fe-B alloy are studied in terms of the correlated-spin-glass approach of Chudnovsky et al.$---- Features predicted by the theory are clearly observed in the experiment. It is shown that the magnetization law may be presented in the form where it is determined by the dimensionless correlation function of structural disorder, C(y), only. The analysis of the magnetization curve allows one to distinguish between different models of disorder in amorphous solids. Experimental data on Dy-Fe-B are in favor of C=exp(-1/2y 2 )
Electron spin echo study of the E'-center phase relaxation in γ-irradiated quartz glass
International Nuclear Information System (INIS)
Dudkin, V.I.; Petrun'kin, V.Yu.; Rubinov, S.V.; Uspenskij, L.I.
1986-01-01
Experimental studies of phase relaxation of E'-centres in γ-irradiated quartz glass are conducted by the method of electron spin echo (ESE) for different concentrations of paramagnetic centres. Contribution of mechanisms of spectral and prompt diffusion to kinetics of amplitude drop of echo signal is proved to reduce with growth of delay time between exciting microwave pulse that results in increase of phase memory time at large delays. The mentioned property can be used in electric controlled delay lines on the base of ESE
Structural features of spin-coated thin films of binary AsxS100−x chalcogenide glass system
International Nuclear Information System (INIS)
Cook, J.; Slang, S.; Golovchak, R.; Jain, H.; Vlcek, M.; Kovalskiy, A.
2015-01-01
Spin-coating technology offers a convenient method for fabricating photostable chalcogenide glass thin films that are especially attractive for applications in IR optics. In this paper we report the structure of spin-coated As x S 100−x (x = 30, 35, 40) thin films as determined using high resolution X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy, especially in relation to composition (i.e. As/S ratio) and preparation process variables. It was observed that As atoms during preparation have a tendency to precipitate out in close to stoichiometric compositions. The mechanism of bonding between the inorganic matrix and organic residuals is discussed based on the experimental data. A weak interaction between S ions and amine-based clusters is proposed as the basis of structural organization of the organic–inorganic interface. - Highlights: • As–S spin-coated chalcogenide thin films with different As/S were fabricated. • XPS measurements support the cluster-like structure of spin-coated films. • As 2 O 3 was confirmed as the composition of precipitate formed during dissolution. • Lack of As–As bonds explains the observed photostability of the thin films
High temperature spin-glass-like transition in La0.67Sr0.33MnO3 nanofibers near the Curie point.
Lu, Ruie; Yang, Sen; Li, Yitong; Chen, Kaiyun; Jiang, Yun; Fu, Bi; Zhang, Yin; Zhou, Chao; Xu, Minwei; Zhou, Xuan
2017-06-28
The glassy transition of superparamagnetic (SPM) (r glass-like (SGL) behavior near the Curie point (T C ), i.e., T 0 = 330 K, in La 0.67 Sr 0.33 MnO 3 (LSMO) nanofibers (NFs) composed of nanoparticles beyond the SPM size (r ≫ r 0 ), resulting in a significant increase of the glass transition temperature. This SGL transition near the T C of bulk LSMO can be explained to be the scenario of locally ordered clusters embedded in a disordered host, in which the assembly of nanoparticles has a magnetic core-shell model driven by surface spin glass. The presence of a surface spin glass of nanoparticles was proved by the Almeida-Thouless line δT f ∝ H 2/3 , exchange bias, and reduced saturation magnetization of the NF system. Composite dynamics were found - that is, both the SPM and the super-spin-glass (SSG) behavior are found in such an NF system. The bifurcation of the zero-field-cooled (ZFC) and field-cooled (FC) magnetization vs. temperature curves at the ZFC peak, and the flatness of FC magnetization involve SSG, while the frequency-dependent ac susceptibility anomaly follows the Vogel-Fulcher law that implies weak dipole interactions of the SPM model. This finding can help us to find a way to search for high temperature spin glass materials.
DEFF Research Database (Denmark)
Dyre, Jeppe
2004-01-01
The temperature dependence of the viscosity of most glassforming liquids is known to depart significantly from the classical Arrhenius behaviour of simple fluids. The discovery of an unexpected correlation between the extent of this departure and the Poisson ratio of the resulting glass could lead...... to new understanding of glass ageing and viscous liquid dynamics....
Two Populations Mean-Field Monomer-Dimer Model
Alberici, Diego; Mingione, Emanuele
2018-04-01
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a variational principle. A detailed analysis is made in the limit of one population is much smaller than the other and a ferromagnetic mean-field phase transition is found.
Exotic nuclei in self-consistent mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.
1999-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics
Modification of linear response theory for mean-field approximations
Hütter, M.; Öttinger, H.C.
1996-01-01
In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the
Reentrant spin glass behavior in polycrystalline La0.7Sr0.3Mn1-XFeXO 3
Directory of Open Access Journals (Sweden)
Xavier Jr. M.M.
2004-01-01
Full Text Available The magnetic and transport properties of the compound La0.7Sr0.3Mn1-xFe xO 3 (0.1 < x <0.4 have been studied by means of electrical resistivity, AC magnetic susceptibility, and DC magnetization. At low concentrations (x <0.1, the system displays essentially para-to-ferromagnetic transitions as the temperature is decreased, although a decrease in the magnetic moment has been observed in previous studies at temperatures a little below T C. This ferromagnetism is explained by double exchange theory in terms of the formation of Mn+3/Mn+4 ions pairs in the system. At concentrations in the range 0.1 < x <0.4 the system is more complex. Increased Fe doping not only weakens the ferromagnetic (FM order and augments the resistivity of the samples, but also induces the appearance of a reentrant spin glass phase at low temperatures (T < 60 K. Irreversibility of the magnetization measured with zero field cooling and with field cooling has been observed. In addition, the AC susceptibility peak position varies with frequency. All these effects are characteristic of spin glass behavior. The results have been interpreted based in an increase of frustration due to increasing competition between FM Mn+3/Mn+4 interactions and antiferromagnetic interactions between ions at the boundaries of Fe clusters.
Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.
2018-02-01
We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.
Saoudi, M; Fritzsche, H; Nieuwenhuys, G J; Hesselberth, M B S
2008-02-08
We used polarized neutron reflectometry to determine the temperature dependence of the magnetization of thin AuFe films with 3% Fe concentration. We performed the measurements in a large magnetic field of 6 T in a temperature range from 295 to 2 K. For the films in the thickness range from 500 to 20 nm we observed a Brillouin-type behavior from 295 K down to 50 K and a constant magnetization of about 0.9 micro(B) per Fe atom below 30 K. However, for the 10 nm thick film we observed a Brillouin-type behavior down to 20 K and a constant magnetization of about 1.3 micro(B) per Fe atom below 20 K. These experiments are the first to show a finite-size effect in the magnetization of single spin-glass films in large magnetic fields. Furthermore, the ability to measure the deviation from the paramagnetic behavior enables us to prove the existence of the spin-glass state where other methods relying on a cusp-type behavior fail.
On Social Optima of Non-Cooperative Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit
2016-12-12
This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
Mean Field Games for Stochastic Growth with Relative Utility
Energy Technology Data Exchange (ETDEWEB)
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Mean Field Games for Stochastic Growth with Relative Utility
International Nuclear Information System (INIS)
Huang, Minyi; Nguyen, Son Luu
2016-01-01
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Energy Technology Data Exchange (ETDEWEB)
Lyubutin, I.S.; Korotkov, N. Yu.; Frolov, K.V. [Shubnikov Institute of Crystallography, RAS, 119333 Moscow (Russian Federation); Kazak, N.V.; Platunov, M.S. [Kirensky Institute of Physics, SB of RAS, 660036 Krasnoyarsk (Russian Federation); Knyazev, Yu. V. [Siberian Federal University, 660074 Krasnoyarsk (Russian Federation); Bezmaternykh, L.N. [Kirensky Institute of Physics, SB of RAS, 660036 Krasnoyarsk (Russian Federation); Ovchinnikov, S.G. [Kirensky Institute of Physics, SB of RAS, 660036 Krasnoyarsk (Russian Federation); Siberian Federal University, 660074 Krasnoyarsk (Russian Federation); Siberian State Aerospace University, 660014 Krasnoyarsk (Russian Federation); Arauzo, A. [Servicio de Medidas Físicas, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain); Bartolomé, J. [Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza and Departamento de Física de la Materia Condensada, 50009 Zaragoza (Spain)
2015-09-05
Highlights: • Spin-glass behavior of MgFeBO{sub 4} and CoFeBO{sub 4} observed by Mössbauer spectroscopy. • Transition temperature T{sub SG} increases strongly with Co substitution. • Dynamical scaling theory near T{sub SG} is fulfilled. • Spin-glass behavior is explained as due to short range correlations. • Inclusion of Co increases exchange interaction and magnetocrystalline anisotropy. - Abstract: Single crystals of MgFeBO{sub 4} and CoFeBO{sub 4} warwickites were obtained. The effects of charge ordering and magnetic properties were investigated by Mössbauer spectroscopy. Cation distribution over M1 and M2 nonequivalent sites and the average charge at the metal positions were established. Low temperature Mössbauer spectra reveal spin-glass behavior, with spin-freezing temperatures T{sub SG} of 15.2 and 33.2 K for Mg- and Co-warwickites, respectively, higher than that observed from the d.c. and a.c. magnetic susceptibility measurements. The difference is explained in terms of dynamical scaling theory. The specific shape of the Mössbauer spectra in the vicinity of the magnetic transition at T{sub SG} shows the difference between spin-glass and superparamagnetic behavior and demonstrates an overwhelming role of the exchange anisotropy in the properties of Mg-warwickite. In Co-warwickite the increase of magnetocrystalline anisotropy provokes an increase in magnetic viscosity.
Some approximate calculations in SU2 lattice mean field theory
International Nuclear Information System (INIS)
Hari Dass, N.D.; Lauwers, P.G.
1981-12-01
Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)
Socio-economic applications of finite state mean field games
Gomes, Diogo A.; Machado Velho, Roberto; Wolfram, Marie Therese
2014-01-01
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-01-01
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.; Saú de, Joã o
2013-01-01
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Mean-field theory of nuclear structure and dynamics
International Nuclear Information System (INIS)
Negele, J.W.
1982-01-01
The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission
Wang, Wenlong; Mandrà, Salvatore; Katzgraber, Helmut
We propose a patch planting heuristic that allows us to create arbitrarily-large Ising spin-glass instances on any topology and with any type of disorder, and where the exact ground-state energy of the problem is known by construction. By breaking up the problem into patches that can be treated either with exact or heuristic solvers, we can reconstruct the optimum of the original, considerably larger, problem. The scaling of the computational complexity of these instances with various patch numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and quantum annealing on the D-Wave 2X quantum annealer. The method can be useful for benchmarking of novel computing technologies and algorithms. NSF-DMR-1208046 and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via MIT Lincoln Laboratory Air Force Contract No. FA8721-05-C-0002.
Re-entrant spin glass and stepped magnetization in mixed-valence SrFe3(PO4)3
International Nuclear Information System (INIS)
Shang Mingyu; Chen Yan; Tian Ge; Yuan Hongming; Feng Shouhua
2013-01-01
The 2 D channel mixed-valent iron (II/III) monophosphate SrFe 3 (PO 4 ) 3 was synthesized via one step mild hydrothermal method at 210 °C and characterized by X-ray diffraction techniques and magnetization measurements. Coexistence of antiferromagnetic superexchange and ferromagnetic superexchange interactions was supposed to be in the lattice according to the Goodenough-Kanamori-Anderson rules. Temperature dependent DC magnetization measurement shows that SrFe 3 (PO 4 ) 3 is ferrimagnet with three magnetic transitions between 2 and 350 K. Through AC magnetization measurement, re-entrant spin glass was observed due to the competition between ferromagnetic and antiferromagnetic interactions. Furthermore, an interesting field induced stepped magnetization was observed in SrFe 3 (PO 4 ) 3 at 2 K with the saturation magnetization Ms=2.4 μ B /f.u. at 5 T.
Non-Fermi liquid and spin-glass behavior of the Sc1-xUxPd3 system
International Nuclear Information System (INIS)
Gajewski, D.A.; Allenspach, P.; Seaman, C.L.; Maple, M.B.
1994-01-01
Previous electrical resistivity ρ(T), magnetic susceptibility χ(T), and specific heat C(T) measurements on the Y 1-x U x Pd 3 system have revealed Kondo behavior for 0 K , where T K is the Kondo temperature: ρ(T)/ρ(0)∼1-T/(aT K ) and C(T)/T∼-(1/T K )ln T with evidence for a finite T=0 residual entropy S(0)=(R/2)ln(2). We report measurements of ρ(T), χ(T), and C(T) on the Sc 1-x U x Pd 3 system which reveal similar Kondo, non-Fermi liquid, and spin-glass behaviors. ((orig.))
Nikolic, V.; Perovic, M.; Kusigerski, V.; Boskovic, M.; Mrakovic, A.; Blanusa, J.; Spasojevic, V.
2015-03-01
Spherical γ-Fe2O3 nanoparticles with the narrow size distribution of (5 ± 1) nm were synthesized by the method of thermal decomposition from iron acetyl acetonate precursor. The existence of super spin-glass state at low temperatures and in low applied magnetic fields was confirmed by DC magnetization measurements on a SQUID magnetometer. The comprehensive investigation of magnetic relaxation dynamics in low-temperature region was conducted through the measurements of single-stop and multiple stop ZFC memory effects, ZFC magnetization relaxation, and AC susceptibility measurements. The experimental findings revealed the peculiar change of magnetic relaxation dynamics at T ≈ 10 K, which arose as a consequence of simultaneous existence of different relaxation processes in Fe2O3 nanoparticle system. Complementarity of the applied measurements was utilized in order to single out distinct relaxation processes as well as to elucidate complex relaxation mechanisms in the investigated interacting nanoparticle system.
DEFF Research Database (Denmark)
Lampert, Felix; Jensen, Annemette H.; Din, Rameez U.
2018-01-01
Spin-on-glass deposition was investigated as viable alternative to increase the durability and performance of 316L steel in chloride environment. The buildup of a detrimental interface oxide was prevented by non-oxidative thermal curing of the coatings, which leads to a transformation...... silica. Electrochemical analysis by cyclic polarization indicated that the coatings behave as imperfect barrier coatings, which may enhance the passive properties of the substrates; however, there is still some statistical scatter in the quality of the coatings. While there is a tendency for an increase...... of the upper limit of the breakdown potential, there is also a decrease of the lower limit. It was found that such lower quality coatings showed, in association with substrate defects, unevenly distributed coating flaws, which may act as initiation points of pitting corrosion and decrease the corrosion...
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-01
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
International Nuclear Information System (INIS)
van Dongen, J.C.M.; van Dijk, D.; Mydosh, J.A.
1981-01-01
Through low-field ac susceptibility measurements we have determined the depression of the superconducting transition temperature T/sub c/ in palladium hydride (T/sub c/0 = 9.3 K) as a function of impurity concentration x for Cr, Mn, and Fe. For Cr and Fe similar values for the initial T/sub c/ depression were found, i.e., -150 K/at. % Cr and -145 K/at. % Fe. From resistivity experiments we are able to estimate the Kondo temperatures T/sub K/, i.e., T/sub K/approx. =10 K for Cr and T/sub K/approx. =5 K for Fe. Since i.e., T/sub K/approx. =10 K for Cr and T/sub K/approx. =5 K for Fe. Since systems exhibits an enhanced pair breaking as described by the theory of Mueller-Hartmann and Zittartz. In contrast, for Mn the initial T/sub c/ depression is -21 K/at. % and T/sub K/<< T/sub c/0, as can be concluded from our resistivity measurements. This means that Mn in PdH exhibits a temperature-independent pair breaking of the Abrikosov and Gor'kov type. However, at larger Mnx values a shoulder appears in T/sub c/(x). We interpret this enhanced superconductivity, according to the theory of Soukoulis and Grest, as being due to the onset of time correlations and short-range antiferromagnetic ordering between the Mn moments. These interaction effects are a precursor to the spin-glass freezing at a lower temperature T/sub f/. Our results suggest a favorable coexistance of superconductivity with the spin-glass state
A mean-field approach for an intercarrier interference canceller for OFDM
International Nuclear Information System (INIS)
Sakata, A; Kabashima, Y; Peleg, Y
2012-01-01
The similarity of the mathematical description of random-field spin systems to the orthogonal frequency-division multiplexing (OFDM) scheme for wireless communication is exploited in an intercarrier interference (ICI) canceller used in the demodulation of OFDM. The translational symmetry in the Fourier domain generically concentrates the major contribution of ICI from each subcarrier in the subcarrier’s neighbourhood. This observation in conjunction with the mean-field approach leads to the development of an ICI canceller whose necessary cost of computation scales linearly with respect to the number of subcarriers. It is also shown that the dynamics of the mean-field canceller are well captured by a discrete map of a single macroscopic variable, without taking the spatial and time correlations of estimated variables into account. (paper)
Skyrme-Hartree-Fock in the realm of nuclear mean field models
International Nuclear Information System (INIS)
Reinhard, P.G.; Reiss, C.; Maruhn, J.; Bender, M.; Buervenich, T.; Greiner, W.
2000-01-01
We discuss and compare two brands of nuclear mean field models, the Skyrme-Hartree-Fock scheme (SHF) and the relativistic mean field model (RMF). Similarities and differences are worked out on a formal basis and with respect to the models performance in describing nuclear data. The bulk observables of stable nuclei are all described very well. Differences come up when extrapolating to exotic nuclei. The typically larger asymmetry energy in RMF leads to a larger neutron skin. Superheavy nuclei are found to be very sensitive on the single particle levels particularly on the spin orbit splitting. Ground state correlations from collective surface vibrations can have a significant effect on difference observables, as two-nucleon separation energy and two-nucleon shell gap. (author)
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-12-04
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Momentum and density dependence of the nuclear mean field
International Nuclear Information System (INIS)
Behera, B.; Routray, T.R.
1999-01-01
The purpose of this is to analyse the momentum, density and temperature dependence of the mean field in nuclear matter derived from finite range effective interactions and to examine the influence of the functional form of the interaction on the high momentum behaviour of the mean field. Emphasis will be given to use very simple parametrizations of the effective interaction with a minimum number of adjustable parameters and yet capable of giving a good description of the mean field in nuclear matter over a wide range of momentum, density and temperature. As an application of the calculated equation of state of nuclear matter, phase transitions to quark-gluon plasma is studied where the quark phase is described by a zeroth order bag model equation of state
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Mean field strategies induce unrealistic nonlinearities in calcium puffs
Directory of Open Access Journals (Sweden)
Guillermo eSolovey
2011-08-01
Full Text Available Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs. To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic nonlinear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.
Self-consistent mean-field models for nuclear structure
International Nuclear Information System (INIS)
Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
2003-01-01
The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications
Back-reaction beyond the mean field approximation
International Nuclear Information System (INIS)
Kluger, Y.
1993-01-01
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N f expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N f is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e + e - plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N f expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation
A Maximum Principle for SDEs of Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Andersson, Daniel, E-mail: danieand@math.kth.se; Djehiche, Boualem, E-mail: boualem@math.kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)
2011-06-15
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
A Maximum Principle for SDEs of Mean-Field Type
International Nuclear Information System (INIS)
Andersson, Daniel; Djehiche, Boualem
2011-01-01
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
International Nuclear Information System (INIS)
Elliott, J.H.
1983-01-01
This thesis reports on three separate investigations in solid state physics. The first is electron paramagnetic resonance in the spin glass Ag:Mn. EPR measurements were performed at two resonance frequencies, concentrating on temperatures above the glass transition temperature. The measured linewidth appears to diverge at T/sub g/ for low resonance frequencies. These results will be compared with recently proposed phenomenological and microscopic theories. The second topic reported in this thesis is the superconducting transition of thin aluminum films. These films were investigated as a function of grain size and thickness. The transition temperature was enhanced over the bulk value, in agreement with many previous investigations of granular aluminum. The third topic reported in this thesis is an extension of the variable rate hopping theory applied in one dimension to N-ME-Qn(TCNQ) 2 . This model is a classical one used to explain both the dc and ac electrical conductivity of organic conductors. The temperature dependence of the model does not agree with experiment at low temperatures. Tunneling has been added to the hopping. This increases the conductivity at low temperatures, and results in excellent agreement with the experimental conductivity over the measured temperature range. The model also predicts that the frequency dependence of the conductivity varies as ω/sup .5/ at low frequencies. This long time tail prediction agrees with the measured dielectric constant of N-Me-iso-Qn(TCNQ) 2
Highly optimized simulations on single- and multi-GPU systems of the 3D Ising spin glass model
Lulli, M.; Bernaschi, M.; Parisi, G.
2015-11-01
We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: (i) the implementation of efficient memory access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); (ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and (iii) a multi-GPU version based on a combination of MPI and CUDA streams. Cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes.
Spin-glass like behaviour in the nanoporous Fe{sub 2}O{sub 3} with amorphous structure
Energy Technology Data Exchange (ETDEWEB)
Thakur, M; Majumdar, S; Giri, S [Department of Solid State Physics and Center for Advanced Materials, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India); Bhaumik, A; Nandi, M [Department of Materials Science and Center for Advanced Materials, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India); Nakamura, H; Kobayashi, H; Kohara, T [Graduate School of Material Science, University of Hyogo, Kamigori, Ako-gun, Hyogo 678-1297 (Japan)], E-mail: sspsg2@iacs.res.in
2008-07-23
The porous Fe{sub 2}O{sub 3} was synthesized chemically. The average size of the particle was {approx}85.0 nm, which was observed by scanning electron microscopy. The signature of porous structure was confirmed by a N{sub 2} adsorption/desorption isotherm and intense x-ray powder diffraction peak at low angle. The x-ray diffraction pattern at high angle indicates the amorphous structure. Moessbauer investigations show that the value of the hyperfine field is {approx}498.0 kOe at 4.2 K which is much smaller than that of the hyperfine field of crystalline {alpha}/{gamma}-Fe{sub 2}O{sub 3} and consistent with the values of amorphous Fe{sub 2}O{sub 3}. The temperature dependence of zero-field cooled magnetization exhibits a peak at 18.0 K (T{sub f}), where T{sub f} follows the Almeida-Thouless relation as T{sub f} {proportional_to} H{sup 2/3}. The ageing phenomenon of the magnetic relaxation below T{sub f} and the memory effect in the field-cooled magnetization indicate the typical features of the classical spin-glass compounds below the spin freezing temperature at T{sub f}.
Symplectic manifolds, coadjoint orbits, and Mean Field Theory
International Nuclear Information System (INIS)
Rosensteel, G.
1986-01-01
Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit
A mean field theory of coded CDMA systems
International Nuclear Information System (INIS)
Yano, Toru; Tanaka, Toshiyuki; Saad, David
2008-01-01
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems
A mean field theory of coded CDMA systems
Energy Technology Data Exchange (ETDEWEB)
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Shapes and dynamics from the time-dependent mean field
International Nuclear Information System (INIS)
Stevenson, P.D.; Goddard, P.M.; Rios, A.
2015-01-01
Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case
Many-Body Mean-Field Equations: Parallel implementation
International Nuclear Information System (INIS)
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Socio-economic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese
2014-11-13
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.
1981-12-01
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
Read, N.
2018-01-01
We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, which have mean zero and variance 1/|i -j | 2 σ, between the spins at sites i and j for all i ≠j . It is known that, for σ >1 , there is no phase transition at any nonzero temperature in this model. We prove rigorously that, for σ >3 /2 , any translation-covariant Newman-Stein metastate for the ground states (i.e., the frequencies with which distinct ground states are observed in finite-size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: One is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all σ >1 , that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for σ >3 /2 . In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values σ >1 /2 . Triviality of the metastate in bond-diluted power-law models for σ >1 is proved directly.
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Massachusetts Inst. of Tech., Cambridge
1981-01-01
In collaboration with Shimon Levit and Zvi Paltiel, significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples will be summarized here. (orig./HSI)
Applying Mean-Field Approximation to Continuous Time Markov Chains
Kolesnichenko, A.V.; Senni, Valerio; Pourranjabar, Alireza; Remke, A.K.I.; Stoelinga, M.I.A.
2014-01-01
The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found
Mean-field theory of anyons near Bose statistics
International Nuclear Information System (INIS)
McCabe, J.; MacKenzie, R.
1992-01-01
The validity of a mean-field approximation for a boson-based free anyon gas near Bose statistics is shown. The magnetic properties of the system is discussed in the approximation that the statistical magnetic field is uniform. It is proved that the anyon gas does not exhibit a Meissner effect in the domain of validity the approximation. (K.A.) 7 refs
Constrained deterministic leader-follower mean field control
Möller, L.; Gentile, B.; Parise, F.; Grammatico, S.; Lygeros, J.
2016-01-01
We consider a mean field game among a large population of noncooperative agents divided into two categories: leaders and followers. Each agent is subject to heterogeneous convex constraints and minimizes a quadratic cost function; the cost of each leader is affected by the leaders' aggregate
A mean-field game economic growth model
Gomes, Diogo A.; Lafleche, Laurent; Nurbekyan, Levon
2016-01-01
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha; Ferreira, Rita; Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Halo nuclei studied by relativistic mean-field approach
International Nuclear Information System (INIS)
Gmuca, S.
1997-01-01
Density distributions of light neutron-rich nuclei are studied by using the relativistic mean-field approach. The effective interaction which parameterizes the recent Dirac-Brueckner-Hartree-Fock calculations of nuclear matter is used. The results are discussed and compared with the experimental observations with special reference to the neutron halo in the drip-line nuclei. (author)
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha
2016-10-04
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
New mean-field calculations for the phase diagram of the Annni model
International Nuclear Information System (INIS)
Tome, T.; Salinas, S.R.A.
1987-01-01
A variational procedure, with the inclusion of some spin fluctuations, to go beyond the standard layer-by-layer mean-field calculations for the T-p phase diagram of the ANNNI model is used. The high temperature region is studied analytically. The transition lines meet smoothly at the Lifshitz point, which is an inflection point of the second-order paramagnetic border. At low temperature, these numerical resuls confirm the stability of the main commensurate phases and show a quantitative trend towards the preductions f the Monte Carlo analyses. (author) [pt
A mean field study of the quasi-one-dimensional antiferromagnetic anisotropic Heisenberg model
International Nuclear Information System (INIS)
Benyoussef, A.
1996-10-01
The effect of the chain and the dimer anisotropies on the ground state energy and the energy gap of the spin-1/2 quasi-one-dimensional antiferromagnetic Heisenberg model is investigated using a mean field theory. The dependence of the magnetization and the effective hopping parameters on the anisotropy α xy (=J xy perpendicular /J xy parallel ) are presented for several values of the chain anisotropy. However, such a system exhibits a transition from antiferromagnetic ordered to disordered phases for arbitrary chain anisotropy and dimer anisotropy. (author). 22 refs, 11 figs
A mean field approach to the Ising chain in a transverse magnetic field
Osácar, C.; Pacheco, A. F.
2017-07-01
We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.
Glass-like recovery of antiferromagnetic spin ordering in a photo-excited manganite Pr0.7Ca0.3MnO3
Energy Technology Data Exchange (ETDEWEB)
Zhou, S. Y.; Langner, M. C.; Zhu, Y.; Chuang, Y. -D.; Rini, M.; Glover, T. E.; Hertlein, M. P.; Gonzalez, A.G. Cruz; Tahir, N.; Tomioka, Y.; Tokura, Y.; Hussain, Z.; Schoenlein, R. W.
2014-01-16
Electronic orderings of charges, orbitals and spins are observed in many strongly correlated electron materials, and revealing their dynamics is a critical step toward understanding the underlying physics of important emergent phenomena. Here we use time-resolved resonant soft x-ray scattering spectroscopy to probe the dynamics of antiferromagnetic spin ordering in the manganite Pr0:7Ca0:3MnO3 following ultrafast photo-exitation. Our studies reveal a glass-like recovery of the spin ordering and a crossover in the dimensionality of the restoring interaction from quasi-1D at low pump fluence to 3D at high pump fluence. This behavior arises from the metastable state created by photo-excitation, a state characterized by spin disordered metallic droplets within the larger charge- and spin-ordered insulating domains. Comparison with time-resolved resistivity measurements suggests that the collapse of spin ordering is correlated with the insulator-to-metal transition, but the recovery of the insulating phase does not depend on the re-establishment of the spin ordering.
Heavy-ion interactions in relativistic mean-field models
International Nuclear Information System (INIS)
Rashdan, M.
1996-01-01
The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....
Nuclear collective vibrations in extended mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Condition monitoring with Mean field independent components analysis
DEFF Research Database (Denmark)
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...... a novelty approach we may detect unseen faulty signals as indeed faulty with high precision, even though the model learns only from normal signals. This is done by evaluating the likelihood that the model generated the signals and adapting a simple threshold for decision. Acoustic emission energy signals...... from a large diesel engine is used to demonstrate this approach. The results show that mean field independent components analysis gives a better detection of fault compared to principal components analysis, while at the same time selecting a more compact model...
Retardation and dispersive effects in the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Davies, K.T.R.; Satchler, G.R.
1993-01-01
We consider several parametrizations of the energy dependence of the imaginary part of the mean field, for nucleons as well as heavy ions. These parametrizations specify the energy dependence of the corresponding real part, because the real and imaginary parts are connected by a dispersion relation. The latter can be viewed as equivalent to the causality property. Since Hilbert transforms appear in the dispersion relation and since Fourier transforms give the correspondence between energy dependence and temporal nonlocality, we derive several properties of these transforms which are of particular interest in the present context. The most useful one is that the Fourier transform of a function F(E) which is analytic in the upper half of the complex E-plane can be expressed in terms of the Fourier transform of the imaginary part of F(E) alone. We investigate several schematic models for the mean field. They fall into two main categories. These correspond to the two main definitions which have been proposed for the mean field, namely the self-energy and Feshbach's potential. Both of these definitions can be used for the nucleon-nucleus system, in which case they correspond to two different ways of handling the combined influence of ground state correlations and antisymmetrization. The resulting two mean fields have different energy dependences and, correspondingly, temporal nonlocalities. Feshbach's approach can also be applied to the nucleus-nucleus system. Our schematic models are semi-realistic, in the sense that they all take account of the 'Fermi surface anomaly' for the nucleon-nucleus system or of the 'threshold anomaly' for the nucleus-nucleus case. The temporal nonlocality is investigated for each model. A physical interpretation of this nonlocality is given in terms delay of the response of the medium, in which an incident wave is partially trapped in nonelastic channels and subsequently reemitted. (orig./HSI)
RPA correlations and nuclear densities in relativistic mean field approach
International Nuclear Information System (INIS)
Van Giai, N.; Liang, H.Z.; Meng, J.
2007-02-01
The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach. (authors)
Probabilistic theory of mean field games with applications
Carmona, René
2018-01-01
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...
Multi-layered metal nanocrystals in a sol-gel spin-on-glass matrix for flash memory applications
Energy Technology Data Exchange (ETDEWEB)
Huang, Meiyu Stella [Department of Chemical and Biomolecular Engineering, National University of Singapore, Block E5, 4 Engineering Drive 4, 117576 (Singapore); Globalfoundries Singapore Pte Ltd, 60 Woodlands Industrial Park D, 738406 (Singapore); Suresh, Vignesh [Department of Chemical and Biomolecular Engineering, National University of Singapore, Block E5, 4 Engineering Drive 4, 117576 (Singapore); Agency for Science, Technology and Research - A*Star, Institute of Materials Research and Engineering (IMRE), #08-03, 2 Fusionopolis Way, Innovis, 138634 (Singapore); Chan, Mei Yin [School of Materials Science and Engineering (MSE), Nanyang Technological University (NTU), 50 Nanyang Avenue, 639798 (Singapore); Ma, Yu Wei [Globalfoundries Singapore Pte Ltd, 60 Woodlands Industrial Park D, 738406 (Singapore); Lee, Pooi See [School of Materials Science and Engineering (MSE), Nanyang Technological University (NTU), 50 Nanyang Avenue, 639798 (Singapore); Krishnamoorthy, Sivashankar [Agency for Science, Technology and Research - A*Star, Institute of Materials Research and Engineering (IMRE), #08-03, 2 Fusionopolis Way, Innovis, 138634 (Singapore); Science et Analyse des Materiaux Unit (SAM), Centre de Recherche Public-Gabriel Lippmann, 41, rue du Brill, Belvaux, 4422 (Luxembourg); Srinivasan, M.P., E-mail: srinivasan.madapusi@rmit.edu.au [Department of Chemical and Biomolecular Engineering, National University of Singapore, Block E5, 4 Engineering Drive 4, 117576 (Singapore); School of Engineering, RMIT University, Building 10, Level 11, Room 14, 376-392 Swanston Street, Melbourne, Victoria, 3001 (Australia)
2017-01-15
A simple and low-cost process of embedding metal nanocrystals as charge storage centers within a dielectric is demonstrated to address leakage issues associated with the scaling of the tunnelling oxide in flash memories. Metal nanocrystals with high work functions (nickel, platinum and palladium) were prepared as embedded species in methyl siloxane spin-on-glass (SOG) films on silicon substrates. Sub-10 nm-sized, well-isolated, uniformly distributed, multi-layered nanocrystals with high particle densities (10{sup 11}–10{sup 12} cm{sup −2}) were formed in the films by thermal curing of the spin-coated SOG films containing the metal precursors. Capacitance-Voltage measurements performed on metal-insulator-semiconductor capacitors with the SOG films show that the presence of metal nanocrystals enhanced the memory window of the films to 2.32 V at low operating voltages of ±5 V. These SOG films demonstrated the ability to store both holes and electrons. Capacitance-time measurements show good charge retention of more than 75% after 10{sup 4} s of discharging. This work demonstrates the applicability of the low-cost in-situ sol-gel preparation in contrast to conventional methods that involve multiple and expensive processing steps. - Highlights: • Sub-10 nm sized, well-isolated, uniformly distributed nanoparticle based charge trap memories. • Preparation of multi-layer high work function metal nanocrystals at low cost. • Large memory window of 2.32 V at low operating voltages of ±5 V. • Good charge retention of more than 90% and 75% after 10{sup 3} and 10{sup 4} s of discharging respectively. • Use of a 3 nm thick tunnelling oxide in compliance with ITRS specifications.
Multi-layered metal nanocrystals in a sol-gel spin-on-glass matrix for flash memory applications
International Nuclear Information System (INIS)
Huang, Meiyu Stella; Suresh, Vignesh; Chan, Mei Yin; Ma, Yu Wei; Lee, Pooi See; Krishnamoorthy, Sivashankar; Srinivasan, M.P.
2017-01-01
A simple and low-cost process of embedding metal nanocrystals as charge storage centers within a dielectric is demonstrated to address leakage issues associated with the scaling of the tunnelling oxide in flash memories. Metal nanocrystals with high work functions (nickel, platinum and palladium) were prepared as embedded species in methyl siloxane spin-on-glass (SOG) films on silicon substrates. Sub-10 nm-sized, well-isolated, uniformly distributed, multi-layered nanocrystals with high particle densities (10"1"1–10"1"2 cm"−"2) were formed in the films by thermal curing of the spin-coated SOG films containing the metal precursors. Capacitance-Voltage measurements performed on metal-insulator-semiconductor capacitors with the SOG films show that the presence of metal nanocrystals enhanced the memory window of the films to 2.32 V at low operating voltages of ±5 V. These SOG films demonstrated the ability to store both holes and electrons. Capacitance-time measurements show good charge retention of more than 75% after 10"4 s of discharging. This work demonstrates the applicability of the low-cost in-situ sol-gel preparation in contrast to conventional methods that involve multiple and expensive processing steps. - Highlights: • Sub-10 nm sized, well-isolated, uniformly distributed nanoparticle based charge trap memories. • Preparation of multi-layer high work function metal nanocrystals at low cost. • Large memory window of 2.32 V at low operating voltages of ±5 V. • Good charge retention of more than 90% and 75% after 10"3 and 10"4 s of discharging respectively. • Use of a 3 nm thick tunnelling oxide in compliance with ITRS specifications.
Electric resistivity of Y (Fe1-xAlx)2 compounds in the spin glass region (0,10
International Nuclear Information System (INIS)
Souza, G.P. de.
1985-01-01
Measurements of electric resistivity in function of the temperature (1.5 1-x Al x2 pseudobinary intermetallic compounds in the region of concentration where there is a spin-glass behaviour, were carried out. The obtained results distinguished two behaviours. In certain cocentration, the minimum of resistivity at low temperatures was observed and in the others, a decrease of resistivity with increase of temperature up to environment temperature was found out. Magnetometry measurements, were carried out aiming to determine freezing critical temperature and of the order of long range, making possible to obtain more accurate measurements in the temperature range where the spin-glass, ferromagnetic and paramagnetic states occur in the compounds. (M.C.K.) [pt
Spin glass behavior in nanogranular La{sub 0.25}Ca{sub 0.75}MnO{sub 3} manganites
Energy Technology Data Exchange (ETDEWEB)
Fernández-Martínez, Antoni [Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN" 2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain); García-Santiago, Antoni, E-mail: agarciasan@ub.edu [Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN" 2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain); Hernàndez, Joan Manel [Grup de Magnetisme, Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, planta 4, edifici nou, 08028 Barcelona (Spain); Institut de Nanociència i Nanotecnologia IN" 2UB, Universitat de Barcelona, Martí i Franquès 1, planta 3, edifici nou, 08028 Barcelona (Spain); Zhang, Tao [Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2014-06-01
The magnetic properties of two nanogranular La{sub 0.25}Ca{sub 0.75}MnO{sub 3} manganites with different average grain sizes have been studied. Besides the well-known exchange bias effect and the appearance of ferromagnetic clusters in the grains of both samples, the results show the occurrence of an antiferromagnetic transition and spin-glass properties. Both samples are described as core–shell magnetic systems, whose main difference is found in the interface between the outer ferromagnetic and the inner antiferromagnetic phases of the grains. - Highlights: • Nanogranular manganites show antiferromagnetism in magnetic measurements. • Exchange bias effect was observed in magnetic hysteresis cycles. • Spin-glass properties were detected at low temperatures. • A core-shell model was applied to describe the results in both samples. • These features have nothing to do with usual properties of nanoparticle manganites.
DEFF Research Database (Denmark)
Jönsson, P. E.; Felton, S.; Svedlindh, P.
2001-01-01
The effect of applied magnetic fields on the collective nonequilibrium dynamics of a strongly interacting Fe-C nanoparticle system has been investigated. It is experimentally shown that the magnetic aging diminishes to finally disappear for fields of moderate strength. The field needed to remove ...... the observable aging behavior increases with decreasing temperature. The same qualitative behavior is observed in an amorphous metallic spin glass (Fe0.15Ni0.85)(75)P16B6Al3....
Wang, Bo-Kun; Wu, Shao-Yi; Yuan, Zi-Yi; Liu, Zi-Xuan; Jiang, Shi-Xin; Liu, Zheng; Yao, Zi-Jian; Teng, Bao-Hua; Wu, Ming-He
2016-08-01
The spin Hamiltonian parameters and local structures are theoretically studied for Cu2+-doped alkaline earth lead zinc phosphate (RPPZ, R=Mg, Ca, Sr, and Ba) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d9 cluster. The relative elongation ratios are found to be ρ≈3.2%, 4.4%, 4.6%, and 3.3% for R=Mg, Ca, Sr, and Ba, respectively, because of the Jahn-Teller effect. The whole decreasing crystal-field strength Dq and orbital reduction factor k from Mg to Sr are ascribed to the weakening electrostatic coulombic interactions and the increasing probability of productivity of nonbridge oxygen (and hence increasing Cu2+-O2- electron cloud admixtures) under PbO addition, respectively, with increasing alkali earth ionic radius. The anomalies (the largest Dq and the next highest k among the systems) for R=Ba are attributed to the cross linkage of this large cation in the network. The overall increasing order (Mg≤Bacontaining copper dopants.
Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling
Sepehrinia, Reza; Chalangari, Fartash
2018-03-01
The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on a distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.
Derivation of mean-field dynamics for fermions
International Nuclear Information System (INIS)
Petrat, Soeren
2014-01-01
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const.N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hartree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schroedinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N→∞. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermionic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const.N and with long-range interactions of
Dipolar ferromagnets and glasses (invited)
International Nuclear Information System (INIS)
Rosenbaum, T.F.; Wu, W.; Ellman, B.; Yang, J.; Aeppli, G.; Reich, D.H.
1991-01-01
What is the ground state and what are the dynamics of 10 23 randomly distributed Ising spins? We have attempted to answer these questions through magnetic susceptibility, calorimetric, and neutron scattering studies of the randomly diluted dipolar-coupled Ising magnet LiHo x Y 1-x F 4 . The material is ferromagnetic for dipole concentrations at least as low as x=0.46, with a Curie temperature obeying mean-field scaling relative to that of pure LiHoF 4 . In the dilute spin limit, an x=0.045 crystal shows very unusual glassy properties characterized by decreasing barriers to relaxation as T→0. Its properties are consistent with a single low degeneracy ground state with a large gap for excitations. A slightly more concentrated x=0.167 sample, however, supports a complex ground state with no appreciable gap, in accordance with prevailing theories of spin glasses. The underlying causes of such disparate behavior are discussed in terms of random clusters as probed by neutron studies of the x=0.167 sample. In addition to tracing the evolution of the glassy and ferromagnetic states with dipole concentration, we investigate the effects of a transverse magnetic field on the Ising spin glass, LiHo 0.167 Y 0.833 F 4 . The transverse field mixes the eigenfunctions of the ground-state Ising doublet with the otherwise inaccessible excited-state levels. We observe a rapid decrease in the characteristic relaxation times, large changes in the spectral form of the relaxation, and a depression of the spin-glass transition temperature with the addition of quantum fluctuations
The mean field in many body quantum physics
International Nuclear Information System (INIS)
Llano, M. de
1984-01-01
As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)
Applicability of self-consistent mean-field theory
International Nuclear Information System (INIS)
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-01-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Surface incompressibility from semiclassical relativistic mean field calculations
International Nuclear Information System (INIS)
Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del
2002-01-01
By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made
First-order, stationary mean-field games with congestion
Evangelista, David
2018-04-30
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
Mean-field theory and self-consistent dynamo modeling
International Nuclear Information System (INIS)
Yoshizawa, Akira; Yokoi, Nobumitsu
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Mean field dynamics of some open quantum systems.
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of [Formula: see text]. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit [Formula: see text], of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Relativistic mean field calculations in neutron-rich nuclei
Energy Technology Data Exchange (ETDEWEB)
Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)
2014-08-14
Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.
Mean-field theory for a ferroelectric transition
International Nuclear Information System (INIS)
Dobry, A.; Greco, A.; Stachiotti, M.
1990-01-01
For the treatment of anharmonic models of solids presenting structural transitions, a commonly used approximation is that of self-consistent phonons. Rather than the usual site decoupling, this mean-field theory is based on decoupling of modes in reciprocal space. A self-consistent phonon approximation for the non-linear polarizability model is developed in this work. The model describes the dynamical properties of ferroelectric materials. Phase diagrams as a function of relevant model parameters are presented. An analysis is made of critical behaviour and it is shown that the approximation leads to the same anomalies found in other models. (Author). 9 refs., 3 figs
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.; Pimentel, Edgard
2015-01-01
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Mean-field level analysis of epidemics in directed networks
Energy Technology Data Exchange (ETDEWEB)
Wang, Jiazeng [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Liu, Zengrong [Mathematics Department, Shanghai University, Shanghai 200444 (China)], E-mail: wangjiazen@yahoo.com.cn, E-mail: zrongliu@online.sh.cn
2009-09-04
The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.
Mean-field level analysis of epidemics in directed networks
International Nuclear Information System (INIS)
Wang, Jiazeng; Liu, Zengrong
2009-01-01
The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.
Mean field dynamics of some open quantum systems
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of √{N }. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit N →∞ , of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
First-order, stationary mean-field games with congestion
Evangelista, David; Ferreira, Rita; Gomes, Diogo A.; Nurbekyan, Levon; Voskanyan, Vardan K.
2018-01-01
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
Surface spin glass and exchange bias effect in Sm0.5Ca0.5MnO3 manganites nano particles
Directory of Open Access Journals (Sweden)
S. K. Giri
2011-09-01
Full Text Available In this letter, we report that the charge/orbital order state of bulk antiferromagnetic Sm0.5Ca0.5MnO3 is suppressed and confirms the appearance of weak ferromagnetism below 65 K followed by a low temperature spin glass like transition at 41 K in its nano metric counterpart. Exchange anisotropy effect has been observed in the nano manganites and can be tuned by the strength of the cooling magnetic field (Hcool. The values of exchange fields (HE, coercivity (HC, remanence asymmetry (ME and magnetic coercivity (MC are found to strongly depend on cooling magnetic field and temperature. HE increases with increasing Hcool but for larger Hcool, HE tends to decrease due to the growth of ferromagnetic cluster size. Magnetic training effect has also been observed and it has been analyzed thoroughly using spin relaxation model. A proposed phenomenological core-shell type model is attributed to an exchange coupling between the spin-glass like shell (surrounding and antiferromagnetic core of Sm0.5Ca0.5MnO3 nano manganites mainly on the basis of uncompensated surface spins. Results suggest that the intrinsic phase inhomogeneity due to the surface effects of the nanostructured manganites may cause exchange anisotropy, which is of special interests for potential application in multifunctional spintronic devices.
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.
1981-01-01
A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures
The application of mean field theory to image motion estimation.
Zhang, J; Hanauer, G G
1995-01-01
Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.
Pairing gaps from nuclear mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Maruhn, J.A.
2000-01-01
We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Misawa, Takahiro; Mori, Sumito [Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020 (Japan); Komine, Takashi [Faculty of Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511 (Japan); Fujioka, Masaya; Nishii, Junji [Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020 (Japan); Kaiju, Hideo, E-mail: kaiju@es.hokudai.ac.jp [Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020 (Japan)
2016-12-30
Graphical abstract: This paper presents the first demonstration of the formation of Ni{sub 78}Fe{sub 22} thin films sandwiched between low-softening-point (LSP) glasses used in spin quantum cross (SQC) devices and the theoretical prediction of spin filter effect in Ni{sub 78}Fe{sub 22}-based SQC devices. The fomation of the LSP-glass/Ni{sub 78}Fe{sub 22}/LSP-glass structures was successfully demonstrated using a newly proposed thermal pressing technique. Interestingly, this technique gives rise to both a highly-oriented crystal growth in Ni{sub 78}Fe{sub 22} thin films and a 100-fold enhancement in coercivity, in contrast to those of as-deposited Ni{sub 78}Fe{sub 22} thin films. This remarkable increase in coercivity can be explained by the calculation based on two-dimensional random anisotropy model. These excellent features on structural and magnetic properties allowed us to achieve that the stray magnetic field was uniformly generated from the Ni{sub 78}Fe{sub 22} thin-film edge in the direction perpendicular to the cross section of the LSP-glass/Ni{sub 78}Fe{sub 22}/LSP-glass structures. As we calculated the stray magnetic field generated between the two edges of Ni{sub 78}Fe{sub 22} thin-film electrodes in SQC devices, a high stray field of approximately 5 kOe was generated when the gap distance between two edges of the Ni{sub 78}Fe{sub 22} thin-film electrodes was less than 5 nm and the thickness of Ni{sub 78}Fe{sub 22} was greater than 20 nm. These experimental and calculated results suggest that Ni{sub 78}Fe{sub 22} thin films sandwiched between LSP glasses can be used as electrodes in SQC devices, providing a spin-filter effect, and also our proposed techniques utilizing magnetic thin-film edges will open up new opportunities for the creation of high performance spin devices, such as large magnetoresistance devices and nanoscale spin injectors. Our paper is of strong interest to the broad audience of Applied Surface Science, as it demonstrates that the
Out-of-equilibrium dynamical mean-field equations for the perceptron model
Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco
2018-02-01
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.
Phase diagrams of the ternary alloy with a single-ion anisotropy in the mean-field approximation
International Nuclear Information System (INIS)
Dely, J.; Bobak, A.
2006-01-01
The phase diagram of the AB p C 1-p ternary alloy consisting of Ising spins S A =32, S B =2, and S C =52 is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The effect of the single-ion anisotropy on the phase diagrams is discussed by changing values of the parameters in the model Hamiltonian and comparison is made with the recently reported finite-temperature phase diagrams for the ternary alloy having spin S B =1
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Mean field theory of dynamic phase transitions in ferromagnets
International Nuclear Information System (INIS)
Idigoras, O.; Vavassori, P.; Berger, A.
2012-01-01
We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H b )-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.
A Stochastic Maximum Principle for General Mean-Field Systems
International Nuclear Information System (INIS)
Buckdahn, Rainer; Li, Juan; Ma, Jin
2016-01-01
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Coalescing colony model: Mean-field, scaling, and geometry
Carra, Giulia; Mallick, Kirone; Barthelemy, Marc
2017-12-01
We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth, and is also of great interest for modeling urban sprawl. Assuming the primary colony to be always circular of radius r (t ) and the emission rate proportional to r (t) θ , where θ >0 , we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ , and compare our results with numerical simulations. We then critically test the validity of the circular approximation for the colony shape and show that it is sound for a constant emission rate (θ =0 ). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony cannot be discarded, thus modifying the scaling exponents.
Mean-field games with logistic population dynamics
Gomes, Diogo A.; De Lima Ribeiro, Ricardo
2013-01-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Relativistic mean field theory for deformed nuclei with pairing correlations
International Nuclear Information System (INIS)
Geng, Lisheng; Toki, Hiroshi; Sugimoto, Satoru; Meng, Jie
2003-01-01
We develop a relativistic mean field (RMF) description of deformed nuclei with pairing correlations in the BCS approximation. The treatment of the pairing correlations for nuclei whose Fermi surfaces are close to the threshold of unbound states needs special attention. With this in mind, we use a delta function interaction for the pairing interaction to pick up those states whose wave functions are concentrated in the nuclear region and employ the standard BCS approximation for the single-particle states obtained from the BMF theory with deformation. We apply the RMF + BCS method to the Zr isotopes and obtain a good description of the binding energies and the nuclear radii of nuclei from the proton drip line to the neutron drip line. (author)
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.
2018-04-01
Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.
Displacement Convexity for First-Order Mean-Field Games
Seneci, Tommaso
2018-05-01
In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between players. Our aim is to extend the concept of displacement convexity from optimal transport to MFGs. This extension gives new estimates for solutions of MFGs. First, we introduce the Monge-Kantorovich problem and examine related results on rearrangement maps. Next, we present the concept of displacement convexity. Then, we derive first-order MFGs, which are given by a system of a Hamilton-Jacobi equation coupled with a transport equation. Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.
A Stochastic Maximum Principle for General Mean-Field Systems
Energy Technology Data Exchange (ETDEWEB)
Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)
2016-12-15
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese
2014-01-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Mean field instabilities in dissipative heavy ion collisions
International Nuclear Information System (INIS)
Colonna, M.; Guarnera, A.; Istituto Nazionale di Fisica Nucleare, Bologna; Catania Univ.; Di Torro, M.; Catania Univ.
1995-01-01
We discuss new reaction mechanisms that may occur in semi-peripheral heavy ion collisions at intermediate energies. In particular we focus on the dynamics of the overlapping zone, showing the development of neck instabilities, coupled with the possibility of an increasing amount amount of dynamical fluctuations. In a very selected beam energy range between 40 and 70 MeV/u we observe an important interplay between stochastic nucleon exchange and the random nature of nucleon-nucleon collisions. Expected consequences are intermediate mass fragment emissions from the neck region and large variances in the projectile-like and target-like observables. The crucial importance of a time matching between the growth of mean field instabilities and the separation of the interacting system is stressed. Some hints towards the observation of relatively large instability effects in deep inelastic collisions at lower energy are finally suggested. (authors). 29 refs., 5 figs., 2 tabs
Low-temperature formation of high-quality gate oxide by ultraviolet irradiation on spin-on-glass
International Nuclear Information System (INIS)
Usuda, R.; Uchida, K.; Nozaki, S.
2015-01-01
Although a UV cure was found to effectively convert a perhydropolysilazane (PHPS) spin-on-glass film into a dense SiO x film at low temperature, the electrical characteristics were never reported in order to recommend the use of PHPS as a gate-oxide material that can be formed at low temperature. We have formed a high-quality gate oxide by UV irradiation on the PHPS film, and obtained an interface midgap trap density of 3.4 × 10 11 cm −2 eV −1 by the UV wet oxidation and UV post-metallization annealing (PMA), at a temperature as low as 160 °C. In contrast to the UV irradiation using short-wavelength UV light, which is well known to enhance oxidation by the production of the excited states of oxygen, the UV irradiation was carried out using longer-wavelength UV light from a metal halide lamp. The UV irradiation during the wet oxidation of the PHPS film generates electron-hole pairs. The electrons ionize the H 2 O molecules and facilitate dissociation of the molecules into H and OH − . The OH − ions are highly reactive with Si and improve the stoichiometry of the oxide. The UV irradiation during the PMA excites the electrons from the accumulation layer, and the built-in electric field makes the electron injection into the oxide much easier. The electrons injected into the oxide recombine with the trapped holes, which have caused a large negative flat band voltage shift after the UV wet oxidation, and also ionize the H 2 O molecules. The ionization results in the electron stimulated dissociation of H 2 O molecules and the decreased interface trap density
Low-temperature formation of high-quality gate oxide by ultraviolet irradiation on spin-on-glass
Energy Technology Data Exchange (ETDEWEB)
Usuda, R.; Uchida, K.; Nozaki, S., E-mail: nozaki@ee.uec.ac.jp [Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-1515 (Japan)
2015-11-02
Although a UV cure was found to effectively convert a perhydropolysilazane (PHPS) spin-on-glass film into a dense SiO{sub x} film at low temperature, the electrical characteristics were never reported in order to recommend the use of PHPS as a gate-oxide material that can be formed at low temperature. We have formed a high-quality gate oxide by UV irradiation on the PHPS film, and obtained an interface midgap trap density of 3.4 × 10{sup 11 }cm{sup −2} eV{sup −1} by the UV wet oxidation and UV post-metallization annealing (PMA), at a temperature as low as 160 °C. In contrast to the UV irradiation using short-wavelength UV light, which is well known to enhance oxidation by the production of the excited states of oxygen, the UV irradiation was carried out using longer-wavelength UV light from a metal halide lamp. The UV irradiation during the wet oxidation of the PHPS film generates electron-hole pairs. The electrons ionize the H{sub 2}O molecules and facilitate dissociation of the molecules into H and OH{sup −}. The OH{sup −} ions are highly reactive with Si and improve the stoichiometry of the oxide. The UV irradiation during the PMA excites the electrons from the accumulation layer, and the built-in electric field makes the electron injection into the oxide much easier. The electrons injected into the oxide recombine with the trapped holes, which have caused a large negative flat band voltage shift after the UV wet oxidation, and also ionize the H{sub 2}O molecules. The ionization results in the electron stimulated dissociation of H{sub 2}O molecules and the decreased interface trap density.
Energy Technology Data Exchange (ETDEWEB)
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
Magnetic structure of a nanoparticle in mean-field approximation
International Nuclear Information System (INIS)
Usov, N.A.; Gudoshnikov, S.A.
2005-01-01
Quantum mechanical Hartree-Fock approximation is used to calculate a magnetic state of a nanoparticle. The cases of ferromagnetic (FM), antiferromagnetic (AFM) and composite particles having an FM core surrounded by an AFM shell are considered in a unified manner. It is shown that effective interaction at the boundary between FM and AFM areas rotates FM and AFM spins perpendicular to each other. The coercive force of a composite particle increases as a function of the AFM shell thickness
International Nuclear Information System (INIS)
Joy, Lija K.; Anantharaman, M.R.; Thomas, Senoy
2013-01-01
Single phase rare earth manganites have attracted scientific interest due to their interesting magnetic, electrical and structural properties. Bulk GdMnO 3 has metamagnetic features with a transition from antiferromagnetic to weak-ferromagnetic state upon cooling. Recently we have found promising magnetic behaviour when GdMnO 3 is doped with strontium. Magnetic behaviour of doped rare earth manganites in the form of Gd 1-x SrMnO 3 has attracted scientific interest due to their promising technological applications in data storage, as catalysts, as electrode materials and sensors. Irreversibility and sharp anomalies has been observed in the magnetization studies of polycrystalline Gd 0.99 Sr 0.01 MnO 3 perovskite synthesized by wet solid state reaction method. X-ray diffraction pattern of the system confirms the single phase orthorhombically distorted perovskite structure. The Field Cooled (FC) and Zero Field Cooled (ZFC) magnetization obtained as a function of temperature with external magnetic field 25Oe, 50Oe, and 200Oe showed thermal irreversibility along with a cusp below the ordering temperature indicating the appearance of spin glass state. The origin of this spin glass state is attributed to spin frustrations, due to the rare earth ions forming a deformed Kagome lattice. Under a magnetic field of 25Oe, the splitting between FC and ZFC magnetization is observed at 70K with a cusp in M ZFC at 45K and when the field is increased to 50Oe and 200Oe, the splitting becomes narrower and shows a shift in the irreversible temperature (T irr ) to lower temperatures 59K and 50K respectively. The spins are frozen in random directions due to a lack of long range magnetic interactions, when the system is cooled through its freezing temperature T f to T f . Room temperature variation of magnetization with applied field indicates the existence of ferromagnetic clusters of glass over antiferromagnetic background. Thermal irreversibility between FC and ZFC below T irr with a
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.
Aging, rejuvenation, and memory effects in short-range Ising spin glass: Cu_0.5Co_0.5Cl_2-FeCl3 GBIC
Suzuki, M.; Suzuki, I. S.
2004-03-01
Cu_0.5Co_0.5Cl_2-FeCl3 GBIC undergoes a spin glass (SG) transition at Tg (= 3.92 ± 0.11 K). The system shows a dynamic behavior that has some similarities and some significant differences compared to a 3D Ising SG.^1 Here we report on non-equilibrium aging dynamics which has been studied using zero-field cooled (ZFC) magnetization and low frequency AC magnetic susceptibility.^2 The time dependence of the relaxation rate S(t) = (1/H)dM_ZFC/dln t for the ZFC magnetization after the ZFC aging protocol, shows a peak at a characteristic time t_cr near a wait time t_w, corresponding to a crossover from quasi equilibrium dynamics to non-equilibrium. The time t_cr strongly depends on t_w, temperature, magnetic field, and the temperature shift. The rejuvenation effect is observed in both i^' and i^'' under the T-shift and H-shift procedures. The memory of the specific spin configurations imprinted during the ZFC aging protocol can be recalled when the system is re-heated at a constant heating rate. The aging, rejuvenation, and memory effects are discussed in terms of the scaling concepts derived from numerical studies on 3D Edwards-Anderson spin glass model. 1. I.S. Suzuki and M. Suzuki, Phys. Rev. B 68, 094424 (2003) 2. M. Suzuki and I.S. Suzuki, cond-mat/0308285
σ-SCF: A direct energy-targeting method to mean-field excited states.
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D; Van Voorhis, Troy
2017-12-07
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry-a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states-ground or excited-are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H 2 , HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
σ-SCF: A direct energy-targeting method to mean-field excited states
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D.; Van Voorhis, Troy
2017-12-01
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry—a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states—ground or excited—are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
Multiagent model and mean field theory of complex auction dynamics
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Multiagent model and mean field theory of complex auction dynamics
International Nuclear Information System (INIS)
Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng
2015-01-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena. (paper)
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Phase diagram of the mean field model of simplicial gravity
International Nuclear Information System (INIS)
Bialas, P.; Burda, Z.; Johnston, D.
1999-01-01
We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form p(q) = q -β , which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases: elongated (fluid) and crumpled. For β ε (2, ∞) the transition between these two phases is first-order, while for β ε (1, 2) it is continuous. The transition becomes softer when β approaches unity and eventually disappears at β = 1. We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new condensed phase appears in the phase diagram. It bears some similarity to the crinkled phase of simplicial gravity discussed recently in models of gravity interacting with matter fields
One-Dimensional Forward–Forward Mean-Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Derivation and precision of mean field electrodynamics with mesoscale fluctuations
Zhou, Hongzhe; Blackman, Eric G.
2018-06-01
Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.
Superheavy nuclei in the relativistic mean-field theory
International Nuclear Information System (INIS)
Lalazissis, G.A.; Ring, P.; Gambhir, Y.K.
1996-01-01
We have carried out a study of superheavy nuclei in the framework of the relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed. (orig.)
Individual based and mean-field modeling of direct aggregation
Burger, Martin; Haskovec, Jan; Wolfram, Marie-Therese
2013-01-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Trapped Bose gas. Mean-field approximation and beyond
International Nuclear Information System (INIS)
Pitaevskii, L.P.
1998-01-01
The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogoliubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ -function. The equation is classical in its essence but contains the ℎ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc
2016-01-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Mean-field inference of Hawkes point processes
International Nuclear Information System (INIS)
Bacry, Emmanuel; Gaïffas, Stéphane; Mastromatteo, Iacopo; Muzy, Jean-François
2016-01-01
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters. (paper)
Mean-field theory of meta-learning
International Nuclear Information System (INIS)
Plewczynski, Dariusz
2009-01-01
We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents
Spin-glass-like dynamics of ferromagnetic clusters in La0.75Ba0.25CoO3
International Nuclear Information System (INIS)
Kumar, Devendra
2014-01-01
We report a magnetization study of the compound La 0.75 Ba 0.25 CoO 3 where the Ba 2+ doping is just above the critical limit for percolation of ferromagnetic clusters. The field cooled and zero-field cooled (ZFC) magnetization exhibit thermomagnetic irreversibility and the ac susceptibility shows a frequency dependent peak at the ferromagnetic ordering temperature (T C ≈ 203 K) of the clusters. These features indicate the presence of a non-equilibrium state below T C . For the non-equilibrium state, the dynamic scaling of the imaginary part of the ac susceptibility and the static scaling of the nonlinear susceptibility clearly establish a spin-glass-like cooperative freezing of ferromagnetic clusters at 200.9(2) K. The assertion of the occurrence of spin-glass-like freezing of ferromagnetic clusters is further substantiated by ZFC ageing and memory experiments. We also observe certain dynamical features which are not present in a typical spin glass, such as: the initial magnetization after ZFC ageing first increases and then decreases with the waiting time; and there is an imperfect recovery of relaxation in negative temperature cycling experiments. This imperfect recovery transforms to perfect recovery for concurrent field cycling. Our analysis suggests that these additional dynamical features have their origin in the inter-cluster exchange interaction and cluster size distribution. The inter-cluster exchange interaction above the magnetic percolation level gives a superferromagnetic state in some granular thin films, but our results show the absence of a typical superferromagnetic-like state in La 0.75 Ba 0.25 CoO 3 . (paper)
Song, Shanshan; Dua, Janesha; Arnold, Craig B
2010-03-15
Spin-coating of chalcogenide glass is a low-cost, scalable method to create optical grade thin films, which are ideal for visible and infrared applications. In this paper, we study the influence of annealing on optical parameters of As(2)S(3) films by examining UV-visible and infrared spectroscopy and correlating the results to changes in the physical properties associated with solvent removal. Evaporation of excess solvent results in a more highly coordinated, denser glass network with higher index and lower absorption. Depending on the annealing temperature and time, index values ranging from n = 2.1 to the bulk value (n = 2.4) can be obtained, enabling a pathway to materials optimization.
International Nuclear Information System (INIS)
Gevorkyan, A.S.; Abajyan, H.G.
2011-01-01
We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The short-range interaction complex-classical Hamiltonian was first used for solving this problem. A system of recurrent equations is obtained on the nodes of the spin-chain lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of the advanced Sylvester conditions which allow step by step construct a huge number of stable spin chains in parallel. The distribution functions of different parameters of spin-glass system are constructed from the first principles of the complex classical mechanics by analyzing the calculation results of the 1D SSCs ensemble. It is shown that the behavior of the parameter distributions is quite different depending on the external fields. The energy ensembles and constants of spin-spin interactions are changed smoothly depending on the external field in the limit of statistical equilibrium, while some of them such as the mean value of polarizations of ensemble and parameters of its orderings are frustrated. We have also studied some critical properties of the ensemble of such catastrophes in the Clausius-Mossotti equation depending on the value of the external field. We have shown that the generalized complex-classical approach excludes these catastrophes allowing one to organize continuous parallel computing on the whole region of values of the external field including critical points. A new representation of the partition function based on these investigations is suggested. As opposed to usual definition, this function is a complex one and its derivatives are everywhere defined, including critical points
International Nuclear Information System (INIS)
Zolotukhin, I.V.; Balalaev, S.Yu.
1990-01-01
Relaxation properties of Y 19 Fe 81 spin glass (SG) were investigated by means of internal friction(IF). Relaxation process resulting from transition to SG state was determined at sound range frequencies in amorphous alloy. On the basis of the obtained results concerning IF and magnetic susceptibility it follows, that relaxation of certain part of cluster magnetic moments lies within 10 -5 -10 -3 s limits with 0.11±0.06 eV activation energy. IF technique is shown to be used for investigation into relaxation properties, in particular, for acquisition of data on temperature of transition to SG' state
Energy Technology Data Exchange (ETDEWEB)
Cook, J. [Austin Peay State University, Clarksville, TN 37075 (United States); Slang, S. [Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice (Czech Republic); Golovchak, R. [Austin Peay State University, Clarksville, TN 37075 (United States); Jain, H. [International Materials Institute for New Functionality in Glass, Lehigh University, Bethlehem, PA 18015 (United States); Vlcek, M. [Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice (Czech Republic); Kovalskiy, A., E-mail: kovalskyya@apsu.edu [Austin Peay State University, Clarksville, TN 37075 (United States)
2015-08-31
Spin-coating technology offers a convenient method for fabricating photostable chalcogenide glass thin films that are especially attractive for applications in IR optics. In this paper we report the structure of spin-coated As{sub x}S{sub 100−x} (x = 30, 35, 40) thin films as determined using high resolution X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy, especially in relation to composition (i.e. As/S ratio) and preparation process variables. It was observed that As atoms during preparation have a tendency to precipitate out in close to stoichiometric compositions. The mechanism of bonding between the inorganic matrix and organic residuals is discussed based on the experimental data. A weak interaction between S ions and amine-based clusters is proposed as the basis of structural organization of the organic–inorganic interface. - Highlights: • As–S spin-coated chalcogenide thin films with different As/S were fabricated. • XPS measurements support the cluster-like structure of spin-coated films. • As{sub 2}O{sub 3} was confirmed as the composition of precipitate formed during dissolution. • Lack of As–As bonds explains the observed photostability of the thin films.
Sine-Gordon mean field theory of a Coulomb gas
Energy Technology Data Exchange (ETDEWEB)
Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan
1997-12-31
Full text. The Coulomb gas provides a paradigm for the study of various models of critical phenomena. In particular, it is well known that the two dimensional (2 D). Coulomb gas can be directly used to study the superfluidity transition in {sup 4} He films, arrays of Josephson junctions, roughening transition, etc. Not withstanding its versatility, our full understanding of the most basic model of Coulomb gas, namely an ensemble of hard spheres carrying either positive or negative charges at their center, is still lacking. It is now well accepted that at low density the two dimensional plasma of equal number of positive and negative particles undergoes a Kosterlitz-Thouless (KT) metal insulator transition. This transition is of an infinite order and is characterized by a diverging Debye screening length. As the density of particles increases, the validity of the KT theory becomes questionable and the possibility of the KT transition being replaced by some kind of first order discontinuity has been speculated for a long time. In this work sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean-field free energy is constructed and the corresponding phase diagrams in two and three dimensions are obtained. When analyzed in terms of chemical potential, the sine-Gordon theory predicts the phase diagram topologically identical to the Monte Carlo simulations and a recently developed Debye-Huckel-Bjerrum theory. In 2D, we find that the infinite-order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole insulating phase is mapped onto zero density. (author)
Temperature dependence of magnetic anisotropy and magnetostriction: Beyond the mean-field theory
International Nuclear Information System (INIS)
Millev, Y.; Faehnle, M.
1994-05-01
The first nonvanishing magnetic anisotropy coefficient is calculated as a function of temperature for any spin quantum number and all temperatures below the Curie temperature for the case of face-centred cubic symmetry within the random-phase approximation (RPA). A detailed and instructive comparison between the mean-field and the RPA predictions is carried out. The RPA magnetization curves are also given for the first time for spins S>1/2. Most of the theoretical considerations are quite general as regard lattice type and even decoupling scheme and can thus be applied straightforwardly to other cases of interest. The progress reported here has been attained with the help of a new simplified and improved parametric approach and of a recent calculation of the average occupation number of magnons within the RPA. In particular, the new approach makes unnecessary the solving of integral equations so that the proposed procedure is especially simple and practically versatile in applications to any particular anisotropic material. (author). Refs, 6 figs
Static and dynamic spin fluctuations in the spin glass doping regime in La2-xSrxCuO4+y
International Nuclear Information System (INIS)
Birgeneau, R.J.; Belk, N.; Kastner, M.A.; Keimer, B.; Shirane, G.
1991-01-01
We review the results of neutron scattering studies of the static and dynamic spin fluctuations crystals of La 2-x Sr x CuO 4+δ in the doping regime intermediate between the Neel and superconducting regions. In this regime the in-plane resistance is linear in temperature down to ∼80 K with a crossover due to logarithmic conductance effects at lower temperatures. The static spin correlations are well-described by a simple model in which the inverse correlation length κ(x,T) =κ(x,0) + κ(0,T). The most dramatic new result is the discovery by Keimer et al. that the dynamic spin fluctuations exhibit a temperature dependence which is a simple function of ω/T for temperatures 10 K≤T≤500 K for a wide range of energies. This scaling leads to a natural explanation of a variety of normal state properties of the copper oxides. 21 refs., 4 figs
International Nuclear Information System (INIS)
Gao Ruorui; Zhang Yue; Yu Wei; Xiong Rui; Shi Jing
2012-01-01
MnFe 2 O 4 nano-particles with an average size of about 7 nm were synthesized by the thermal decomposition method. Based on the magnetic hysteresis loops measured at different temperatures the temperature-dependent saturation magnetization (M S ) and coercivity (H C ) are determined. It is shown that above 20 K the temperature-dependence of the M S and H C indicates the magnetic behaviors in the single-domain nano-particles, while below 20 K, the change of the M S and H C indicates the freezing of the spin-glass like state on the surfaces. By measuring the magnetization–temperature (M–T) curves under the zero-field-cooling (ZFC) and field-cooling procedures at different applied fields, superparamagnetism behavior is also studied. Even though in the ZFC M–T curves peaks can be observed below 160 K, superparamagnetism does not appear until the temperature goes above 300 K, which is related with the strong inter-particle interaction. - Highlights: ► MnFe 2 O 4 nano-particles with size of 7 nm were prepared. ► The surface spin-glass like state is frozen below 20 K. ► The peaks in ZFC magnetization–temperature curves are observed below 160 K. ► The inter-particle interaction inhibits the superparamagnetism at room temperature.
Magnetic and magnetocaloric properties of spin-glass material DyNi{sub 0.67}Si{sub 1.34}
Energy Technology Data Exchange (ETDEWEB)
Chen, X. [The Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA 50011-3020 (United States); College of Physics and Electronic Information Engineering, Neijiang Normal University, Neijiang 641100 (China); Mudryk, Y., E-mail: slavkomk@ameslab.gov [The Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA 50011-3020 (United States); Pathak, A.K.; Feng, W. [The Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA 50011-3020 (United States); Pecharsky, V.K. [The Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA 50011-3020 (United States); Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011-2300 (United States)
2017-08-15
Highlights: • Spin-glass state is observed in the DyNi{sub 0.67}Si{sub 1.4} compound. • Random Ni/Si distribution in the AlB{sub 2}-type structure leads to magnetic frustration. • Magnetic frustration affects magnetic field dependence of magnetocaloric effect. - Abstract: Structural, magnetic, and magnetocaloric properties of DyNi{sub 0.67}Si{sub 1.34} were investigated using X-ray powder diffraction, magnetic susceptibility, and magnetization measurements. X-ray powder diffraction pattern shows that DyNi{sub 0.67}Si{sub 1.34} crystallizes in the AlB{sub 2}-type hexagonal structure (space group: P6/mmm, No. 191, a = b = 3.9873(9) Å, and c = 3.9733(1) Å). The compound is a spin-glass with the freezing temperature T{sub G} = 6.2 K. The ac magnetic susceptibility measurements confirm magnetic frustration in DyNi{sub 0.67}Si{sub 1.34}. The maximum value of the magnetic entropy change determined from M(H) data is −16.1 J/kg K at 10.5 K for a field change of 70 kOe.
Kumar, Arun; Kaushik, S. D.; Siruguri, V.; Pandey, Dhananjai
2018-03-01
For disordered Heisenberg systems with small single ion anisotropy (D ), two spin-glass (SG) transitions below the long-range ordered (LRO) phase transition temperature (Tc) have been predicted theoretically for compositions close to the percolation threshold. Experimental verification of these predictions is still controversial for conventional spin glasses. We show that multiferroic spin-glass systems can provide a unique platform for verifying these theoretical predictions via a study of change in magnetoelastic and magnetoelectric couplings, obtained from an analysis of diffraction data, at the spin-glass transition temperatures (TSG). Results of macroscopic (dc M (H , T ), M(t ), ac susceptibility [χ (ω, T )], and specific heat (Cp)) and microscopic (x-ray and neutron scattering) measurements are presented on disordered BiFe O3 , a canonical Heisenberg system with small single ion anisotropy, which reveal appearance of two spin-glass phases, SG1 and SG2, in coexistence with the LRO phase below the Almeida-Thouless (A-T) and Gabey-Toulouse (G-T) lines. It is shown that the temperature dependence of the integrated intensity of the antiferromagnetic (AFM) peak shows dips with respect to the Brillouin function behavior around the SG1 and SG2 transition temperatures. The temperature dependence of the unit cell volume departs from the Debye-Grüneisen behavior below the SG1 transition and the magnitude of departure increases significantly with decreasing temperature up to the electromagnon driven transition temperature below which a small change of slope occurs followed by another similar change of slope at the SG2 transition temperature. The ferroelectric polarization also changes significantly at the two spin-glass transition temperatures. These results, obtained using microscopic techniques, clearly demonstrate that the SG1 and SG2 transitions occur on the same magnetic sublattice and are intrinsic to the system. We also construct a phase diagram showing all
International Nuclear Information System (INIS)
Hojsik, M.; Gmuca, S.
1998-01-01
Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use
Energy Technology Data Exchange (ETDEWEB)
Meyer, Benjamin Michael [Iowa State Univ., Ames, IA (United States)
2003-01-01
As time progresses, the world is using up more of the planet's natural resources. Without technological advances, the day will eventually arrive when these natural resources will no longer be sufficient to supply all of the energy needs. As a result, society is seeing a push for the development of alternative fuel sources such as wind power, solar power, fuel cells, and etc. These pursuits are even occurring in the state of Iowa with increasing social pressure to incorporate larger percentages of ethanol in gasoline. Consumers are increasingly demanding that energy sources be more powerful, more durable, and, ultimately, more cost efficient. Fast Ionic Conducting (FIC) glasses are a material that offers great potential for the development of new batteries and/or fuel cells to help inspire the energy density of battery power supplies. This dissertation probes the mechanisms by which ions conduct in these glasses. A variety of different experimental techniques give a better understanding of the interesting materials science taking place within these systems. This dissertation discusses Nuclear Magnetic Resonance (NMR) techniques performed on FIC glasses over the past few years. These NMR results have been complimented with other measurement techniques, primarily impedance spectroscopy, to develop models that describe the mechanisms by which ionic conduction takes place and the dependence of the ion dynamics on the local structure of the glass. The aim of these measurements was to probe the cause of a non-Arrhenius behavior of the conductivity which has been seen at high temperatures in the silver thio-borosilicate glasses. One aspect that will be addressed is if this behavior is unique to silver containing fast ion conducting glasses. more specifically, this study will determine if a non-Arrhenius correlation time, τ, can be observed in the Nuclear Spin Lattice Relaxation (NSLR) measurements. If so, then can this behavior be modeled with a new single
Long-time predictability in disordered spin systems following a deep quench.
Ye, J; Gheissari, R; Machta, J; Newman, C M; Stein, D L
2017-04-01
We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.
Long-time predictability in disordered spin systems following a deep quench
Ye, J.; Gheissari, R.; Machta, J.; Newman, C. M.; Stein, D. L.
2017-04-01
We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit—in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.
Haule, Kristjan
2018-04-01
The Dynamical Mean Field Theory (DMFT) in combination with the band structure methods has been able to address reach physics of correlated materials, such as the fluctuating local moments, spin and orbital fluctuations, atomic multiplet physics and band formation on equal footing. Recently it is getting increasingly recognized that more predictive ab-initio theory of correlated systems needs to also address the feedback effect of the correlated electronic structure on the ionic positions, as the metal-insulator transition is almost always accompanied with considerable structural distortions. We will review recently developed extension of merger between the Density Functional Theory (DFT) and DMFT method, dubbed DFT+ embedded DMFT (DFT+eDMFT), whichsuccessfully addresses this challenge. It is based on the stationary Luttinger-Ward functional to minimize the numerical error, it subtracts the exact double-counting of DFT and DMFT, and implements self-consistent forces on all atoms in the unit cell. In a few examples, we will also show how the method elucidated the important feedback effect of correlations on crystal structure in rare earth nickelates to explain the mechanism of the metal-insulator transition. The method showed that such feedback effect is also essential to understand the dynamic stability of the high-temperature body-centered cubic phase of elemental iron, and in particular it predicted strong enhancement of the electron-phonon coupling over DFT values in FeSe, which was very recently verified by pioneering time-domain experiment.
Dedes, I.; Dudek, J.
2018-03-01
We examine the effects of the parametric correlations on the predictive capacities of the theoretical modelling keeping in mind the nuclear structure applications. The main purpose of this work is to illustrate the method of establishing the presence and determining the form of parametric correlations within a model as well as an algorithm of elimination by substitution (see text) of parametric correlations. We examine the effects of the elimination of the parametric correlations on the stabilisation of the model predictions further and further away from the fitting zone. It follows that the choice of the physics case and the selection of the associated model are of secondary importance in this case. Under these circumstances we give priority to the relative simplicity of the underlying mathematical algorithm, provided the model is realistic. Following such criteria, we focus specifically on an important but relatively simple case of doubly magic spherical nuclei. To profit from the algorithmic simplicity we chose working with the phenomenological spherically symmetric Woods–Saxon mean-field. We employ two variants of the underlying Hamiltonian, the traditional one involving both the central and the spin orbit potential in the Woods–Saxon form and the more advanced version with the self-consistent density-dependent spin–orbit interaction. We compare the effects of eliminating of various types of correlations and discuss the improvement of the quality of predictions (‘predictive power’) under realistic parameter adjustment conditions.
Effective interactions and mean field theory: from nuclear matter to nuclei
International Nuclear Information System (INIS)
Cochet, B.
2005-07-01
The Skyrme force is a zero-range force that allows the construction of the mean field inside the nucleus in a simple way. Skyrme forces are reasonably predictive but some features of the infinite nuclear matter or the mass of heavy nuclei are not well computed. The aim of this work is to propose an expanded parametrization of the Skyrme force in order to improve its predictive power. The first part is dedicated to the construction of the expansion of the parametrization. We recall how the effective forces are linked to the nucleon-nucleon interaction then we show the limits of the standard Skyrme forces and we propose a relatively natural improvements based on the integration of spin and isospin instabilities. The second part deals with the validation of the model, first by describing infinite nuclear matter then by studying β-balanced nuclear matter which has enabled us to reproduce some features of neutron stars like mass and radius. The computation of properties of nuclei like binding energy, mass, radii depends strongly on the adjustment procedure. (A.C.)
Karaoulanis, D; Bacalis, N C
2000-01-01
We have performed Monte Carlo simulations of magnetic semiconductors above and below the nearest-neighbour percolation threshold (NNPT) using a classical Heisenberg Hamiltonian with up to third nearest-neighbour (nn) interactions. Large clusters were created allowing use of realistically low magnetic fields (10 G). Above NNPT our results, apart from confirming the existing picture of this class of materials, also show that the inclusion of the second and third (nn) interactions increases the frustration, thus making the transition temperature smaller and closer to experiment than calculated via the first nn interactions only. A physically plausible explanation is given. Below NNPT our results strongly support the validity of the hypothesis (D. Karaoulanis, J.P. Xanthakis, C. Papatriantafillou, J. Magn. Magn. Mater. 161 (1996) 231), that the experimentally observed susceptibility is the sum of two contributions: a paramagnetic one due to isolated magnetic clusters, and a spin-glass contribution due to an 'infi...
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-12-01
This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of Λ N and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy ( S Λ, S 2Λ) and two lambda shell gaps ( δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective
International Nuclear Information System (INIS)
Pedro, I de; Rojo, J M; Pizarro, J L; Fernandez, J RodrIguez; Marcos, J Sanchez; Fernandez-DIaz, M T; Arriortua, M I; Rojo, T
2006-01-01
Compounds of the general formula Co 2-x Ni x (OH)PO 4 (x = 0.1, 0.3) have been synthesized under mild hydrothermal conditions. Neutron powder diffraction, susceptibility and heat capacity measurements were carried out on polycrystalline samples. The cobalt-nickel compounds are ordered as three-dimensional antiferromagnets with ordering temperatures of 70 and 64 K for x = 0.1 and x = 0.3, respectively. The magnetic study shows a spin glass-like state below 11 and 5 K for Co 1.9 Ni 0.1 (OH)PO 4 and Co 1.7 Ni 0.3 (OH)PO 4 , respectively. Specific heat data present peaks at 68 and 61 K for Co 1.9 Ni 0.1 and Co 1.7 Ni 0.3 , respectively. These peaks show broad shoulders between approximately 15 and 40 K. The lack of any distinguishable anomaly below 10 K supports the spin glass nature of the low temperature transitions. Refinement of room temperature neutron diffraction data indicates that the Ni(II) ions are in octahedral co-ordination with the practical absence of these ions in the trigonal bipyramidal sites. The magnetic structures of Co 2-x Ni x (OH)PO 4 consist of ferromagnetic arrangements between the octahedral chains and trigonal bipyramidal dimers within the xz plane with the magnetic moments along the z axis. The ferromagnetic layers are disposed antiparallel to one another along the y direction establishing the three-dimensional antiferromagnetic order (T N ∼70 K for Co 1.9 Ni 0.1 and ∼64 K for Co 1.7 Ni 0.3 ). The different exchange pathways, the anisotropy of the Co(II) ions and the frustration of the magnetic moments in the trigonal bipyramidal geometry could be responsible for the freezing process
Energy Technology Data Exchange (ETDEWEB)
Gao Ruorui [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Zhang Yue, E-mail: yue-zhang@mail.hust.edu.cn [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Department of Electric Science and Technology, Huazhong University of Science and Technology, Wuhan 430074 (China); Yu Wei [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Xiong Rui [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Key Laboratory for the Green Preparation and Application of Functional Materials of Ministry of Education, Hubei University, Wuhan 430062 (China); Shi Jing [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Key Laboratory for the Green Preparation and Application of Functional Materials of Ministry of Education, Hubei University, Wuhan 430062 (China); International Center for Material Physics, Shen Yang 110015 (China)
2012-08-15
MnFe{sub 2}O{sub 4} nano-particles with an average size of about 7 nm were synthesized by the thermal decomposition method. Based on the magnetic hysteresis loops measured at different temperatures the temperature-dependent saturation magnetization (M{sub S}) and coercivity (H{sub C}) are determined. It is shown that above 20 K the temperature-dependence of the M{sub S} and H{sub C} indicates the magnetic behaviors in the single-domain nano-particles, while below 20 K, the change of the M{sub S} and H{sub C} indicates the freezing of the spin-glass like state on the surfaces. By measuring the magnetization-temperature (M-T) curves under the zero-field-cooling (ZFC) and field-cooling procedures at different applied fields, superparamagnetism behavior is also studied. Even though in the ZFC M-T curves peaks can be observed below 160 K, superparamagnetism does not appear until the temperature goes above 300 K, which is related with the strong inter-particle interaction. - Highlights: Black-Right-Pointing-Pointer MnFe{sub 2}O{sub 4} nano-particles with size of 7 nm were prepared. Black-Right-Pointing-Pointer The surface spin-glass like state is frozen below 20 K. Black-Right-Pointing-Pointer The peaks in ZFC magnetization-temperature curves are observed below 160 K. Black-Right-Pointing-Pointer The inter-particle interaction inhibits the superparamagnetism at room temperature.
Shlyk, L.; Strobel, S.; Farmer, B.; De Long, L. E.; Niewa, R.
2018-02-01
Single-crystal x-ray diffraction refinements indicate SrS n2F e4O11 crystallizes in the hexagonal R -type ferrite structure with noncentrosymmetric space group P 63m c and lattice parameters a =5.9541 (2 )Å , c =13.5761 (5 )Å , Z =2 (R (F )=0.034 ). Octahedrally coordinated 2 a [M (1) and M (1a)] and 6 c sites [M (2 )] have random, mixed occupation by Sn and Fe; whereas the tetrahedrally coordinated 2 b sites [Fe(3) and Fe(3a)] are exclusively occupied by Fe, whose displacement from the ideal position with trigonal-bipyramidal coordination causes the loss of inversion symmetry. Our dc and ac magnetization data indicate SrS n2F e4O11 single crystals undergo a ferro- or ferri-magnetic transition below a temperature TC=630 K with very low coercive fields μoHc ⊥=0.27 Oe and μoHc ∥=1.5 Oe at 300 K, for applied field perpendicular and parallel to the c axis, respectively. The value for TC is exceptionally high, and the coercive fields exceptionally low, among the known R-type ferrites. Time-dependent dc magnetization and frequency-dependent ac magnetization data indicate the onset of short-range, spin-glass freezing below Tf=35.8 K , which results from crystallographic disorder of magnetic F e3 + and nonmagnetic S n4 + ions on a frustrated Kagome sublattice. Anomalous ac susceptibility and thermomagnetic relaxation behavior in the short-range-ordered state differs from that of conventional spin glasses. Optical measurements in the ultraviolet to visible frequency range in a diffuse reflectance geometry indicate an overall optical band gap of 0.8 eV, consistent with observed semiconducting properties.
Energy Technology Data Exchange (ETDEWEB)
Wang, Bo-Kun; Yuan, Zi-Yi; Liu, Zi-Xuan; Jiang, Shi-Xin; Liu, Zheng; Yao, Zi-Jian [University of Electronic Science and Technology of China, Chengdu (China). School of Yingcai Honors; Wu, Shao-Yi; Teng, Bao-Hua; Wu, Ming-He [University of Electronic Science and Technology of China, Chengdu (China). Dept. of Applied Physics
2016-11-01
The spin Hamiltonian parameters and local structures are theoretically studied for Cu{sup 2+}-doped alkaline earth lead zinc phosphate (RPPZ, R=Mg, Ca, Sr, and Ba) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d{sup 9} cluster. The relative elongation ratios are found to be ρ ∼ 3.2%, 4.4%, 4.6%, and 3.3% for R=Mg, Ca, Sr, and Ba, respectively, because of the Jahn-Teller effect. The whole decreasing crystal-field strength Dq and orbital reduction factor k from Mg to Sr are ascribed to the weakening electrostatic coulombic interactions and the increasing probability of productivity of nonbridge oxygen (and hence increasing Cu{sup 2+}-O{sup 2-} electron cloud admixtures) under PbO addition, respectively, with increasing alkali earth ionic radius. The anomalies (the largest Dq and the next highest k among the systems) for R=Ba are attributed to the cross linkage of this large cation in the network. The overall increasing order (Mg≤Ba
Mean field approximation versus exact treatment of collisions in few-body systems
International Nuclear Information System (INIS)
Lemm, J.; Weiguny, A.; Giraud, B.G.
1990-01-01
A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)
International Nuclear Information System (INIS)
Faria, A.C. de.
1990-01-01
A detailed study of the S-K model through the analysis of the zeros of the partition function in the complex temperature plane is performed. By the exact way, the notable thermodynamical properties of the system to a variety of the length (N=5→25 spins) are calculated, using only standards concepts (without the use of tricks like that of replicas). Dilute models had been also considered. The principal result of this work is the characterization of the zeros of the partition function of the S-K model. (author)
Generating functional of the mean field in quantum electrodynamics with non-stable vacuum
International Nuclear Information System (INIS)
Gitman, D.M.; Kuchin, V.A.
1981-01-01
Generating functional for calculating a mean field, in the case of unstable vacuum, in quantum field theory has been suggested. Continual representation for the generating functional of the mean field has been found in the case of quantum electrodynamics with an external field. Generating electron-positron pairs from vacuum [ru
DEFF Research Database (Denmark)
Lerchner, Alexander; Sterner, G.; Hertz, J.
2006-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn, with a numerical procedure for solving the mean-field equations quantitatively. With our treatment, one can determine self-consistently both the firing rates and the firing correlations...
International Nuclear Information System (INIS)
Schlichting, H.
1985-01-01
We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)
On melting dynamics and the glass transition. II. Glassy dynamics as a melting process.
Krzakala, Florent; Zdeborová, Lenka
2011-01-21
There are deep analogies between the melting dynamics in systems with a first-order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first-order transition--namely p-spin models on the so-called Nishimori line--it can be shown that the melting dynamics can be exactly mapped to the equilibrium dynamics. In this mapping the dynamical--or mode-coupling--glass transition corresponds to the spinodal point, while the Kauzmann transition corresponds to the first-order phase transition itself. Both in mean field and finite dimensional models this mapping provides an exact realization of the random first-order theory scenario for the glass transition. The corresponding glassy phenomenology can then be understood in the framework of a standard first-order phase transition.
Energy Technology Data Exchange (ETDEWEB)
Typel, S; Wolter, H H [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Dynamics of Impurity and Valence Bands in Ga1-xMnxAs Within the Dynamical Mean-Field Approximation
International Nuclear Information System (INIS)
Majidi, M.A.; Moreno, Juana; Jarrell, Mark; Fishman, Randy Scott; Aryanpour, K.A.
2006-01-01
We calculate the density-of-states and the spectral function of Ga 1-x Mn x As within the dynamical mean-field approximation. Our model includes the competing effects of the strong spin-orbit coupling on the J=3/2 GaAs hole bands and the exchange interaction between the magnetic ions and the itinerant holes. We study the quasiparticle and impurity bands in the paramagnetic and ferromagnetic phases for different values of impurity-hole coupling J c at a Mn doping of x=0.05. By analyzing the anisotropic angular distribution of the impurity band carriers at T=0, we conclude that the carrier polarization is optimal when the carriers move along the direction parallel to the average magnetization.
Energy Technology Data Exchange (ETDEWEB)
Juillet, O.; Gulminelli, F. [Caen Univ., Lab. de Physique Corpusculaire (LPC/ENSICAEN), 14 (France); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-11-01
The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For an harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated. (author)
International Nuclear Information System (INIS)
Adam, G.; Adam, S.
2007-01-01
The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T c superconductivity in cuprates rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean-field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, the use of spectral representations allows the identification and elimination of exponentially small quantities. This procedure secures the reduction of the correlation order to the GMFA-GF expressions
On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2
International Nuclear Information System (INIS)
Troudet, T.; Paris-11 Univ., 91 - Orsay
1986-01-01
We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)
Shlyk, Larysa; Strobel, S.; Farmer, B.; De Long, L. E.; Niewa, R.
2018-05-01
Single-crystal x-ray diffraction refinements indicate SrSn2Fe4O11 crystallizes in the hexagonal R-type ferrite structure with non-centrosymmetric space group P63mc and lattice parameters a = 5.9541(2) Å, c = 13.5761(5) Å, Z = 2 (R(F) = 0.034). Octahedrally coordinated sites are randomly occupied by Sn and Fe; whereas tetrahedrally coordinated sites are exclusively occupied by Fe, whose displacement from ideal trigonal-bipyramidal coordination causes the loss of inversion symmetry. DC magnetization data indicate SrSn2Fe4O11 single crystals undergo ferro- or ferri-magnetic order below a transition temperature TC = 630 K with very low coercive fields Hc ⊥ = 0.27 Oe and Hc// = 1.5 Oe at 300 K, for applied fields perpendicular and parallel to the c-axis, respectively. The value for TC is exceptionally high, and the coercive fields exceptionally low, among the known R-type ferrites. Enhanced coercivity and thermomagnetic hysteresis suggest the onset of short-range, spin glass order occurs below Tf = 35 K. Optical measurements indicate a band gap of 0.8 eV, consistent with wide-gap semiconducting behavior and a previously established empirical correlation between the semiconducting gap and TC for R-type ferrites based upon Ru.
International Nuclear Information System (INIS)
Synoradzki, K.; Toliński, T.
2016-01-01
We report on the CeNi_4Mn (ferromagnet FM) - CeCu_4Mn (spin-glass SG) transformation leading to a complex magnetic phase diagram (MPD). It is verified that all the Ce(Cu_1_-_xNi_x)_4Mn alloys are isostructural and the transformation is governed only by the Cu-Ni substitution. MPD is built based on the magnetic dc/ac susceptibility measurements and reveals SG formation as well as the region of the coexistence of the FM and SG state in the middle range of the Ni concentration. The complex MPD is explained by clusters formation and a competition of interactions between various crystallographic sites of the hexagonal CaCu_5-type structure, mainly the 3g-3g and 3g-2c interactions. The predominance of the SG state is confirmed by the analysis of the frequency dependence of the ac magnetic susceptibility components and the relaxation of the remanent magnetization. Additionally, the presence of two multicritical points is observed. - Highlights: • We fully characterized the magnetic properties of Ce(Cu_1_-_xNi_x)_4Mn alloys. • We show the presence of complex magnetic behaviour due to atomic-site disorder. • Magnetic phase diagram revels mixed-phase ground state. • Two multicritical points on magnetic phase diagram occurs.
Energy Technology Data Exchange (ETDEWEB)
Nikolic, V.; Perovic, M., E-mail: mara.perovic@vinca.rs; Kusigerski, V.; Boskovic, M.; Mrakovic, A.; Blanusa, J.; Spasojevic, V. [University of Belgrade, Condensed Matter Physics Laboratory, Institute of Nuclear Sciences Vinca (Serbia)
2015-03-15
Spherical γ-Fe{sub 2}O{sub 3} nanoparticles with the narrow size distribution of (5 ± 1) nm were synthesized by the method of thermal decomposition from iron acetyl acetonate precursor. The existence of super spin-glass state at low temperatures and in low applied magnetic fields was confirmed by DC magnetization measurements on a SQUID magnetometer. The comprehensive investigation of magnetic relaxation dynamics in low-temperature region was conducted through the measurements of single-stop and multiple stop ZFC memory effects, ZFC magnetization relaxation, and AC susceptibility measurements. The experimental findings revealed the peculiar change of magnetic relaxation dynamics at T ≈ 10 K, which arose as a consequence of simultaneous existence of different relaxation processes in Fe{sub 2}O{sub 3} nanoparticle system. Complementarity of the applied measurements was utilized in order to single out distinct relaxation processes as well as to elucidate complex relaxation mechanisms in the investigated interacting nanoparticle system.
Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen
2018-04-01
The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.
Reitz, Christian; Suchomski, Christian; Chakravadhanula, Venkata Sai Kiran; Djerdj, Igor; Jagličić, Zvonko; Brezesinski, Torsten
2013-04-01
Herein, we report the synthesis, microstructure, and magnetic properties of cadmium ferrite (CdFe2O4) thin films with both an ordered cubic network of 18 nm diameter pores and single-phase spinel grains averaging 13 nm in diameter. These mesoporous materials were produced through facile polymer templating of hydrated nitrate salt precursors. Both the morphology and the microstructure, including cation site occupancy and electronic bonding configuration, were analyzed in detail by electron microscopy, grazing incidence small-angle X-ray scattering, Raman and X-ray photoelectron spectroscopy, and N2-physisorption. The obtained data demonstrate that the network of pores is retained up to annealing temperatures as high as 650 °C--the onset of crystallization is at ϑ = (590 ± 10) °C. Furthermore, they show that the polymer-templated samples exhibit a "partially" inverted spinel structure with inversion parameter λ = 0.40 ± 0.02. This differs from microcrystalline CdFe2O4 which shows virtually no inversion. Magnetic susceptibility studies reveal ferrimagnetic spin coupling below 147 K and further point to the likelihood of glassy behavior at low temperature (T(f) ≈ 60 K). In addition, analysis of room temperature magnetization data indicates the presence of sub-10 nm diameter superparamagnetic clusters in an otherwise paramagnetic environment.
Energy Technology Data Exchange (ETDEWEB)
Bhowmik, R.N. [Experimental Condensed Matter Physics Dvision, Saha Institute of Nuclear Physics, Kolkata-70064 (India)]. E-mail: rnb@cmp.saha.ernet.in; Ranganathan, R. [Experimental Condensed Matter Physics Dvision, Saha Institute of Nuclear Physics, Kolkata-70064 (India)]. E-mail: ranga@cmp.saha.ernet.in; Nagarajan, R. [Tata Institute of Fundamental Research, Department of Condensed Matter Physics and Materials Science, Colaba Road, Mumbai (India)
2006-04-15
We discuss our investigation of DC magnetization, as a function of time, temperature and magnetic field, and explore some distinct magnetic behaviour in the polycrystalline spinel Co{sub 0.2}Zn{sub 0.8}Fe{sub 1.95}Ho{sub 0.05}O{sub 4}. The system is essentially to be a ferrimagnet and the ferrimagnetic order (spontaneous magnetization) is identified using Arrot plot of M(H) data. Application of some scaling laws have shown the coexistence of spin glass (SG) and superparamagnetism (SPM) with ferrimagnetic order (FIMO) at low and high temperature, respectively, in the system. The coexistence of SG and SPM with FIMO shows paramagnetic to ferrimagnetic state at T{sub C}{approx}225K and ferrimagnetic to cluster spin glass state below T{sub m}{approx}120K. The non-linear increase, without hysteresis, of M(H) data above T{sub C} indicates the existence of short range interacting clusters in the paramagnetic state. In addition, the anisotropy effect of Ho{sup 3+} has shown some interesting magnetic features, such as, spin glass of Ising nature and an unusual maximum in the thermoremanent magnetization about 180K.
Mean-field theory of active electrolytes: Dynamic adsorption and overscreening
Frydel, Derek; Podgornik, Rudolf
2018-05-01
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou; Vilanova, Pedro; Debbah, Mé roú ane
2012-01-01
nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show
Semiclassical approximations in a mean-field theory with collision terms
International Nuclear Information System (INIS)
Galetti, D.
1986-01-01
Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.; Patrizi, Stefania; Voskanyan, Vardan
2014-01-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana
2017-01-01
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Stochastic mean-field dynamics for fermions in the weak coupling limit
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2005-09-15
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |{phi}{sub a}> <|{phi}{sub b}| / <|{phi}{sub b} | |{phi} {sub a}> where |{phi}{sub a}> and |{phi}{sub b}> are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-01-01
-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose
Stochastic mean-field dynamics for fermions in the weak coupling limit
International Nuclear Information System (INIS)
Lacroix, D.
2005-09-01
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |Φ a > b | / b | |Φ a > where |Φ a > and |Φ b > are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
Desplanques, B.
1986-07-01
We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models
Chen, Lie-Wen; Ko, Che Ming; Li, Bao-An
2007-01-01
Using various relativistic mean-field models, including the nonlinear ones with meson field self-interactions, those with density-dependent meson-nucleon couplings, and the point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compare the results with the constra...
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2015-01-01
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Linear–Quadratic Mean-Field-Type Games: A Direct Method
Directory of Open Access Journals (Sweden)
Tyrone E. Duncan
2018-02-01
Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy
Nandi, Manoj Kumar; Maitra Bhattacharyya, Sarika
2018-01-01
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.
International Nuclear Information System (INIS)
Molina, Joel; Munoz, Ana; Torres, Alfonso; Landa, Mauro; Alarcon, Pablo; Escobar, Manuel
2011-01-01
In this work, the physical, chemical and electrical properties of Metal-Oxide-Semiconductor (MOS) capacitors with Spin-On-Glass (SOG)-based thin films as gate dielectric have been investigated. Experiments of SOG diluted with two different solvents (2-propanol and deionized water) were done in order to reduce the viscosity of the SOG solution so that thinner films (down to ∼20 nm) could be obtained and their general characteristics compared. Thin films of SOG were deposited on silicon by the sol-gel technique and they were thermally annealed using conventional oxidation furnace and Rapid Thermal Processing (RTP) systems within N 2 ambient after deposition. SOG dilution using non-organic solvents like deionized water and further annealing (at relatively high temperatures ≥450 deg. C) are important processes intended to reduce the organic content of the films. Fourier-Transform Infrared (FTIR) Spectroscopy results have shown that water-diluted SOG films have a significant reduction in their organic content after increasing annealing temperature and/or dilution percentage when compared to those of undiluted SOG films. Both current-voltage (I-V) and capacitance-voltage (C-V) measurements show better electrical characteristics for SOG-films diluted in deionized water compared to those diluted in 2-propanol (which is an organic solvent). The electrical characteristics of H 2 O-diluted SOG thin films are very similar to those obtained from high quality thermal oxides so that their application as gate dielectrics in MOS devices is promising. Finally, it has been demonstrated that by reducing the organic content of SOG-based thin films, it is possible to obtain MOS devices with better electrical properties.