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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, exact combinatorial versions of bosonization identities are presented, which equate the product of two Ising correlators with a free field (bosonic) correlator, and the role of the discrete free field is played by the height function of an associated bipartite dimer model.
Abstract: We present exact combinatorial versions of bosonization identities, which equate the product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete free field is played by the height function of an associated bipartite dimer model. Some applications to the asymptotic analysis of Ising correlators are discussed.
111 citations
TL;DR: In this paper, a non-trivial exponent /3 characterising non-equilibrium coarsening processes is calculated in a soluble model, where the exponent describes how the fraction po of spins which have never flipped (or, equivalently, the fraction of space which has never been traversed by a domain wall) depends on the characteristic domain scale L: p, - I/-'.
Abstract: A non-trivial exponent /3 characterising non-equilibrium coarsening processes is calculated in a soluble model. For a spin model, the exponent describes how the fraction po of spins which have never flipped (or, equivalently, the fraction of space which has never been traversed by a domain wall) depends on the characteristic domain scale L: p, - I/-'. For the one-dimensional time-dependent Ginzburg-Landau equation at zero temperature we show that the critical exponent /3 is the zero of a transcendental equation, and find ,8 = 0.824 924 12 ... . Coarsening phenomena are rather common in physics. A typical example is the non- equilibrium evolution of the ordered domains that form when a system is thermally quenched from a homogeneous phase into a two-phase region(l). Other examples include grain growth (2), soap froths (3), and breath figures (4). A common feature of these phenomena is the scale-invariant morphology that develops at late times: the structure at different times is statistically similar apart from an overall change of scale, i.e. the system is described by a single, time-dependent length scale Ut). To fix our ideas, consider one of the simplest such systems-the d = 1 Ising model, with Glauber dynamics, evolved from a random initial condition at temperature T = 0. The behaviour of this system is well understood. The domain walls behave as independent random walkers. When two domain walls meet they annihilate. The average domain size (1) grows as t '1'. The equal-time (5,6) and two-time (5) spin-spin correlation functions can be exactly calculated.
111 citations
TL;DR: It is observed that the interface-free-energy estimates based on CNT are generally in error, and extensive calculations for the Ising model show that corrections due to a nonsharp and thermally fluctuating interface account for the barrier shape with excellent accuracy.
Abstract: We reconsider the applicability of classical nucleation theory (CNT) to the calculation of the free energy of solid cluster formation in a liquid and its use to the evaluation of interface free energies from nucleation barriers. Using two different freezing transitions (hard spheres and NaCl) as test cases, we first observe that the interface-free-energy estimates based on CNT are generally in error. As successive refinements of nucleation-barrier theory, we consider corrections due to a nonsharp solid-liquid interface and to a nonspherical cluster shape. Extensive calculations for the Ising model show that corrections due to a nonsharp and thermally fluctuating interface account for the barrier shape with excellent accuracy. The experimental solid nucleation rates that are measured in colloids are better accounted for by these non-CNT terms, whose effect appears to be crucial in the interpretation of data and in the extraction of the interface tension from them.
111 citations
TL;DR: In this paper, the Wulff construction in three and more dimensions for an Ising model with nearest neighbor interaction was proved in three dimensions. But the construction was not applied to the case of a two-dimensional model.
Abstract: In this paper we prove the Wulff construction in three and more dimensions for an Ising model with nearest neighbor interaction.
111 citations
TL;DR: In this article, the problem of randomly dilute Heisenberg or Ising ferromagnetic lattices is discussed on the basis of expansions of susceptibility in inverse powers of temperature, and the first six significant coefficients in such expansions have been found, for any lattice and any spin value.
Abstract: The problem of a randomly dilute Heisenberg or Ising ferromagnetic is discussed on the basis of expansions of susceptibility in inverse powers of temperature. The first six significant coefficients in such expansions have been found, for any lattice and any spin value. The series are used to estimate the dependence of Curie temperature, ϑ c, on concentration of magnetic elements, p, for simple cubic, body-centred cubic and face-centred cubic lattices and spins ½ and 1. Near p = 1, it is found that for the Ising models ϑ c(p)=p ϑ c(1) whereas for the Heisenberg models ϑ c(p) < p ϑ c(1).
110 citations