Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4621976 | Journal of Mathematical Analysis and Applications | 2007 | 11 Pages |
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.
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