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:10.1155/2009/571950Published: 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.