Research Article
The Stochastic Ising Model with the Mixed Boundary Conditions
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 2009Abstract
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.
