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Boundary Value Problems
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The Stochastic Ising Model with the Mixed Boundary Conditions

Boundary Value Problems volume 2009, Article number: 571950 (2009) Cite this article

Abstract

We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive) boundary conditions are given. Further, at inverse temperatures , we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.

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  1. Department of Mathematics, College of Science, Beijing Jiaotong University, Beijing, 100044, China

    Jun Wang

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  1. Jun Wang
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Correspondence to Jun Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, J. The Stochastic Ising Model with the Mixed Boundary Conditions. Bound Value Probl 2009, 571950 (2009). https://doi.org/10.1155/2009/571950

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  • DOI: https://doi.org/10.1155/2009/571950

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