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Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.


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TL;DR: The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite and the zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed.
Abstract: 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.

122 citations

Journal ArticleDOI
TL;DR: In this paper, a many-body interatomic potential for the Fe-Ni system is fitted, capable of describing both the ferritic and austenitic phase, and the mixing enthalpy and defect properties were fitted.
Abstract: A many-body interatomic potential for the Fe–Ni system is fitted, capable of describing both the ferritic and austenitic phase. The Fe–Ni system exhibits two stable ordered intermetallic phases, namely, L10 FeNi and L12 FeNi3, that are key issues to be tackled when creating a Fe–Ni potential consistent with thermodynamics. A procedure, based on a rigid lattice Ising model and the theory of correlation functions space, is developed to address all the intermetallics that are possible ground states of the system. While controlling the ground states of the system, the mixing enthalpy and defect properties were fitted. Both bcc and fcc defect properties are compared with density functional theory calculations and other potentials found in the literature. Finally, the potential is thermodynamically validated by constructing the alloy phase diagram. It is shown that the experimental phase diagram is reproduced reasonably well and that our potential gives a globally improved description of the Fe–Ni system in the whole concentration range with respect to the potentials found in the literature.

122 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the real-time dynamics of the order parameter σ(t) in the Ising field theory after a quench in the fermion mass, which corresponds to a quen in the transverse field of the corresponding transverse-field Ising chain.
Abstract: We study the real-time dynamics of the order parameter σ(t) in the Ising field theory after a quench in the fermion mass, which corresponds to a quench in the transverse field of the corresponding transverse field Ising chain. We focus on quenches within the ordered phase. The long-time behaviour is obtained analytically by a resummation of the leading divergent terms in a form-factor expansion for σ(t). Our main result is the development of a method for treating divergences associated with working directly in the field theory limit. We recover the scaling limit of the corresponding result by Calabrese et al (2011 Phys. Rev. Lett. 106 227203), which was obtained for the lattice model. Our formalism generalizes to integrable quantum quenches in other integrable models.

122 citations

Journal ArticleDOI
TL;DR: This work proves Russo‐Seymour‐Welsh‐type uniform bounds on crossing probabilities for the FK Ising (FK percolation with cluster weight q = 2) model at criticality, independent of the boundary conditions, and derives several noteworthy properties, among which are the fact that there is no infinite cluster atcriticality, tightness properties for the interfaces, and the existence of several critical exponents.
Abstract: We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising (FK percolation with cluster weight q = 2) model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model [24], which allows us to get precise estimates on boundary connection probabilities. We stay in a discrete setting; in particular, we do not make use of any continuum limit, and our result can be used to derive directly several noteworthy properties—including some new ones—among which are the fact that there is no infinite cluster at criticality, tightness properties for the interfaces, and the existence of several critical exponents, in particular the half-plane, one-arm exponent. Such crossing bounds are also instrumental for important applications such as constructing the scaling limit of the Ising spin field [6] and deriving polynomial bounds for the mixing time of the Glauber dynamics at criticality [17]

121 citations

Journal ArticleDOI
TL;DR: The first exact calculation of the topological pressure for an N-body stochastic interacting system, namely, an infinite-range Ising model endowed with spin-flip dynamics is presented, including a corresponding finite Kolmogorov-Sinai entropy.
Abstract: We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely, an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the KolmogorovSinai and the topological entropies follow. In statistical mechanics, bridging the microscopics to the macroscopics remains the ultimate goal, be it in or out of equilibrium. The development of the theory of dynamical systems and of their chaotic properties has led to major advances in equilibrium and nonequilibrium statistical mechanics. All those approaches make extensive use of such concepts as Lyapunov exponents, Kolmogorov-Sinai (KS) or topological entropies, topological pressure, etc., all quite mathematical in nature, and for which very few results (even nonrigorous) are available, as far as systems with many degrees of freedom are concerned. One of the central ideas in constructing a statistical physics out of equilibrium is that of Gibbs ensembles [1] in which time is seen to play the role of the volume in traditional equilibrium statistical mechanics. A central quantity called the dynamical partition function is, in general, defined as

121 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023682
20221,314
2021854
2020947
2019870
2018844