Boundary Value Problems
Volume 2009 (2009), Article ID 571950, 17 pages
Research Article

The Stochastic Ising Model with the Mixed Boundary Conditions

Department of Mathematics, College of Science, Beijing Jiaotong University, Beijing 100044, China

Received 16 December 2008; Revised 12 April 2009; Accepted 19 June 2009

Academic Editor: Veli Shakhmurov

Copyright © 2009 Jun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.