scispace - formally typeset
Search or ask a question
Topic

Ising model

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


Papers
More filters
Journal ArticleDOI
TL;DR: The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function as discussed by the authors.
Abstract: The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism—a dynamical Gibbs ensemble construction—to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.

319 citations

Journal ArticleDOI
TL;DR: In this paper, the universal form of the susceptibility peak is obtained for two-dimensional Ising models at T = Tc and a method of phenomenological renormalization is suggested and used to estimate universal amplitudes.
Abstract: Finite-size rounding of a first-order phase transition is studied in “block”- and “cylinder”-shaped ferromagnetic scalar spin systems. Crossover in shape is investigated and the universal form of the rounded susceptibility peak is obtained. Scaling forms on the low-temperature side of the critical point are considered both above and below the borderline dimensionality,d >=4. A method of phenomenological renormalization, applicable to both odd and even field derivatives, is suggested and used to estimate universal amplitudes for two-dimensional Ising models atT=Tc.

318 citations

Journal ArticleDOI
TL;DR: In this paper, a generalized Ginzburg-Landau theory is proposed to describe the phase transition of an array of weakly coupled pseudo-one-dimensional chains, which is based on a mean-field approximation.
Abstract: A generalized Ginzburg-Landau theory is suggested to describe the phase transition of an array of weakly coupled pseudo-one-dimensional chains. Using a mean-field approximation, the coupled-chain problem is reduced to that of a single chain in an effective field. The finite-range correlations which develop along the chain are treated using exact one-dimensional solutions. The results obtained are then used to construct a generalized Ginzburg-Landau theory. We argue that this approach provides a means of treating the remaining slowly varying long-range fluctuations. Results are given for a variety of arrays consisting of Ising, classical Heisenberg, real and complex ${\ensuremath{\psi}}^{4}$ chains.

314 citations

Journal ArticleDOI
TL;DR: In this article, the phase diagram of strongly interacting matter as a function of temperature and baryon number density is explored, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons.
Abstract: We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting $ $ and $ $ condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for nonzero current quark mass. A tricritical point separates the first order transition at high densities from the second order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.

313 citations

Journal ArticleDOI
TL;DR: In this article, the critical properties of exactly soluble Ising model on a planar random dynamical lattice representing a regularization of the zero-dimensional string with internal fermions were investigated.

312 citations


Network Information
Related Topics (5)
Hamiltonian (quantum mechanics)
48.6K papers, 1M citations
93% related
Phase transition
82.8K papers, 1.6M citations
91% related
Quantum
60K papers, 1.2M citations
91% related
Ground state
70K papers, 1.5M citations
89% related
Ferromagnetism
55K papers, 1.2M citations
88% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023682
20221,314
2021854
2020947
2019870
2018844