Skip to main content

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

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jun Wang.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Wang, J. The Stochastic Ising Model with the Mixed Boundary Conditions. Bound Value Probl 2009, 571950 (2009). https://doi.org/10.1155/2009/571950

Download citation

Keywords

  • Boundary Condition
  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
\