The Potts model with countable set of spin values on a Cayley tree

Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2006) The Potts model with countable set of spin values on a Cayley tree. Letters in Mathematical Physics, 75 (2). pp. 99-109. ISSN 0377-9017 (P), 1573-0530 (O)

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Abstract

We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k�1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0, 1, . . . } we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give description of the class of measures ν on Φ such that with respect to each element of this class our infinite system of equations has unique solution {ai , i =1, 2, . . . }, where a ∈(0, 1).

Item Type:	Article (Journal)
Additional Information:	4430/14417
Uncontrolled Keywords:	Cayley tree, Countable set, Gibbs measures, Potts model.
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:	31 May 2012 10:33
Last Modified:	31 May 2012 10:33
URI:	http://irep.iium.edu.my/id/eprint/14417

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