The Stochastic Ising Model with the Mixed Boundary Conditions. (19th July 2009)

• Record Type: Journal Article
• Authors: Wang, Jun
• Other Names: Shakhmurov Veli Academic Editor.
• Is Part Of: Boundary value problems. Volume 2009(2009)
• Publication Date: 2009-07-19
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2009/571950
• Languages: English
• ISSNs: 1687-2762

Abstract

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