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  • Research Article
  • Open Access

The Stochastic Ising Model with the Mixed Boundary Conditions

Boundary Value Problems20092009:571950

https://doi.org/10.1155/2009/571950

  • Received: 16 December 2008
  • Accepted: 19 June 2009
  • Published:

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.

Keywords

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

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Authors’ Affiliations

(1)
Department of Mathematics, College of Science, Beijing Jiaotong University, Beijing, 100044, China

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