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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: In this article, the authors show how to combine their earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves.
Abstract: We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves with parameter $\kappa=3$ and $\kappa=16/3$ respectively.

127 citations

Posted Content
TL;DR: In this article, the authors studied discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones, and proved uniform convergence of discrete harmonic measures, Green's functions and Poisson kernels to their continuous counterparts.
Abstract: We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures, Green's functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models.

126 citations

Journal ArticleDOI
TL;DR: In this article, a Coulomb gap was found in the density of states for bare single-particle excitations, which was fitted well by an exponential form proposed by Efros.
Abstract: We have carried out numerical calculations on two- and three-dimensional models of highly localized electrons interacting by an unscreened Coulomb potential. A Coulomb gap was found in the density of states for bare single-particle excitations. This "soft" gap was deeper than the power-law gap seen in earlier simulations, but for three-dimensional systems it was fitted well by an exponential form proposed by Efros. The gap fills as the temperature is raised. We also found an unexpected clustering of states with the same occupation and energies close to the chemical potential. The density of states for dressed single-particle excitations ("electronic polarons") showed a Coulomb gap too, but a narrower one than that for the bare excitations. There is a clear analogy between this model of interacting electrons and an Ising spin-glass with $\frac{1}{r}$ antiferromagnetic interactions and a random field on each site. We have exploited this analogy to search for a glass transition in the electronic system by calculating the specific heat, susceptibility, and a modified Edwards-Anderson order parameter.

126 citations

Journal ArticleDOI
TL;DR: In this article, exact expressions for the n-spin correlation function of the two-dimensional Ising model were obtained for both T > T/sub c/ and T < T/ sub c/ for the case of both T and sub c. The scaling limit of these correlation functions can be shown to exist and yields n-point Schwinger functions of some relativistic quantum field theories.
Abstract: For both T > T/sub c/ and T < T/sub c/, we report exact expressions for the n-spin correlation function of the two-dimensional Ising model suitable for studying large separations between spins. In particular, the scaling limit of these correlation functions can be shown to exist and yields n-point Schwinger functions of some relativistic quantum field theories.

126 citations

Journal ArticleDOI
TL;DR: This article review three socio-economic models of economic opinions, urban segregation, and language change and show that the well-known two-dimensional Ising model gives about the same results in each case.
Abstract: I review three socio-economic models of economic opinions, urban segregation, and language change and show that the well-known two-dimensional Ising model gives about the same results in each case.

126 citations


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