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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 paper, results from percolation theory are used to study phase transitions in one-dimensional Ising and q-state Potts models with couplings of the asymptotic form.
Abstract: Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ
x,y≈ const/¦x−y¦2. For translation-invariant systems with well-defined lim
x→∞
x
2
J
x
=J
+ (possibly 0 or ∞) we establish: (1) There is no long-range order at inverse temperaturesβ withβJ
+⩽1. (2) IfβJ
+>q, then by sufficiently increasingJ
1 the spontaneous magnetizationM is made positive. (3) In models with 0
336 citations
01 Jan 1980
TL;DR: In the last few years, the study of phase transitions in two-dimensional systems has absorbed a great deal of effort by both theorists and experimentalists as discussed by the authors, with the increase of the sensitivity of experiments, which can now be checked by the experimentalists.
Abstract: During the last few years, the study of phase transitions in two dimensional systems has absorbed a great deal of effort by both theorists and experimentalists. Although such an activity is rather esoteric in the sense that these systems are rather special and do not occur in every day life, they are a theorist’s paradise because they form a very special class of systems for which theory is capable of yielding quantitative predictions. With the increase of the sensitivity of experiments, these predictions can now be checked by the experimentalists.
336 citations
Journal Article•
TL;DR: A scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology is presented and is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems.
Abstract: Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.
336 citations
TL;DR: In this article, a general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed, besides the well-known Ising and "ice" models, other soluble cases are also considered.
Abstract: A general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed. Besides the well-known Ising and "ice" models, other soluble cases are also considered. After discussing some general symmetry properties of this model, we consider in detail a particular class of the soluble cases, the "free-fermion" model. The explicit expressions for all thermodynamic functions with the inclusion of an external electric field are obtained. It is shown that both the specific heat and the polarizability of the free-fermion model exhibit in general a logarithmic singularity. An inverse-square-root singularity results, however, if the free-fermion model also satisfies the ice condition. The results are illustrated with a specific example.
335 citations
TL;DR: In this article, the phase transitions in Abelian two-dimensional spin and four-dimensional gauge systems can be understood in terms of condensation of topological objects, i.e., kinks and fluxoids.
Abstract: We show how phase transitions in Abelian two-dimensional spin and four-dimensional gauge systems can be understood in terms of condensation of topological objects. In the spin systems these objects are kinks and in the gauge systems either magnetic monopoles or fluxoids (quantized lines of magnetic flux). Four models are studied: two-dimensional Ising and $\mathrm{XY}$ models and four-dimensional ${Z}_{2}$ and U(1) gauge systems.
334 citations