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

Published: 19 July 2009

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.