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Open Access Research Article

The Stochastic Ising Model with the Mixed Boundary Conditions

Jun Wang

Author Affiliations

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

Boundary Value Problems 2009, 2009:571950  doi:10.1155/2009/571950

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2009/1/571950


Received:16 December 2008
Revisions received:12 April 2009
Accepted:19 June 2009
Published:19 July 2009

© 2009 The Author(s).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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