Open Access

The Stochastic Ising Model with the Mixed Boundary Conditions

Boundary Value Problems20092009:571950

Received: 16 December 2008

Accepted: 19 June 2009

Published: 19 July 2009


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.


Boundary ConditionDifferential EquationPartial Differential EquationOrdinary Differential EquationFunctional Equation

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Authors’ Affiliations

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


© Jun Wang. 2009

This article is published under license to BioMed Central Ltd. 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.