Article ID Journal Published Year Pages File Type
4621976 Journal of Mathematical Analysis and Applications 2007 11 Pages PDF
Abstract

We consider a nearest-neighbor Potts model, with countable spin values Φ={0,1,…}, and nonzero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. The problem is reduced to the description of the solutions of some infinite system of equations. We give full description of the class of probabilistic measures ν on Φ such that our infinite system of equations has unique solution with respect to each element of this class. In particular we describe the Poisson measures which are Gibbsian.

Related Topics
Physical Sciences and Engineering Mathematics Analysis