Boundary Value Problems
Volume 2009 (2009), Article ID 571950, 17 pages
doi:10.1155/2009/571950

The stochastic Ising model with the mixed boundary conditions

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 β>βc, we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.