Journal ArticleDOI
Correlations in Ising Ferromagnets. I
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In this paper, an inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit a spontaneous magnetization at temperatures above the mean-field approximation to the Curie or critical point.Abstract:
An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit a spontaneous magnetization at temperatures above the mean-field approximation to the Curie or “critical” point. (As a consequence, the corresponding “lattice gas” cannot undergo a first order phase transition in density (condensation) above this temperature.) The mean-field susceptibility in zero magnetic field at high temperatures is shown to be an upper bound for the exact result.read more
Citations
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Correlation inequalities on some partially ordered sets
TL;DR: In this article, it was shown that increasing functions on a finite distributive lattice are positively correlated by positive measures satisfying a suitable convexity property, and applications to Ising ferromagnets in an arbitrary magnetic field and to the random cluster model were given.
Journal ArticleDOI
Existence of a phase-transition in a one-dimensional Ising ferromagnet
TL;DR: In this paper, the existence of a phase transition for an infinite linear chain of spins with an interaction energy was proved for the case where ρ is positive and monotone decreasing, and the sums ρJ(n) and ρ (log logn) [n 3 ρ(n)]−1 both converged.
Journal ArticleDOI
Ricci curvature of Markov chains on metric spaces
TL;DR: In this article, the authors define the Ricci curvature of metric spaces in terms of how much small balls are closer (in Wasserstein transportation distance) than their centers are.
Journal ArticleDOI
Sharpness of the phase transition in percolation models
Michael Aizenman,David J. Barsky +1 more
TL;DR: In this paper, the equality of two critical points -the percolation threshold pH and the point pτ where the cluster size distribution ceases to decay exponentially -is proven for all translation invariant independent per-colation models on homogeneous d-dimensional lattices.
Journal ArticleDOI
Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions
TL;DR: The existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions was proved in this article.
References
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Journal ArticleDOI
Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
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Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
T.D. Lee,Chen Ning Yang +1 more
TL;DR: In this paper, the problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent, and an example of a two-dimensional lattice model is given for which the phase transition regions in the $p\ensuremath{-}v$ diagram is exactly calculated.
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Two-Dimensional Ising Model as a Soluble Problem of Many Fermions
TL;DR: In the absence of an external magnetic field, the Onsager method has been shown to be exactly soluble and shows a phase transition as discussed by the authors, which has attracted a lot of interest in the last few decades.
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On Ising's model of ferromagnetism
TL;DR: In this paper, Ising discussed the following model of a ferromagnetic body: Assume N elementary magnets of moment μ to be arranged in a regular lattice; each of them is supposed to have only two possible orientations, which we call positive and negative.
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Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising Ferromagnet
TL;DR: In this article, minor modifications are made in the Peierls argument that a two-dimensional Ising ferromagnet possesses a spontaneous moment at sufficiently low temperatures, in order to make the proof quite rigorous.