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Limiting Gibbs measures of Potts model with countable set of spin values

Ganikhodjaev, Nasir (2007) Limiting Gibbs measures of Potts model with countable set of spin values. Journal of Mathematical Analysis and Applications, 336 (1). pp. 693-703. ISSN 0022-247X

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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.

Item Type: Article (Journal)
Additional Information: 4430/1645
Uncontrolled Keywords: Cayley tree; Countable set; Gibbs measure; Potts model; Poisson measure
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Prof. Nasir Ganikhodjaev
Date Deposited: 18 Nov 2011 14:16
Last Modified: 21 Nov 2011 22:20
URI: http://irep.iium.edu.my/id/eprint/1645

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