Open Access

The Stochastic Ising Model with the Mixed Boundary Conditions

Boundary Value Problems20092009:571950

DOI: 10.1155/2009/571950

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.

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Authors’ Affiliations

Department of Mathematics, College of Science, Beijing Jiaotong University


© Jun Wang. 2009

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