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On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model

Mukhamedov, Farrukh (2009) On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model. Proceedings of the Steklov Institute of Mathematics, 265 (1). pp. 165-176. ISSN 0081-5438

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Abstract

We consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized p-adic Gibbs measures. Note that the condition found does not depend on the values of the prime p, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition.

Item Type: Article (Journal)
Additional Information: 5537/13695
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes: Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 03 Jan 2012 11:03
Last Modified: 03 Jan 2012 11:03
URI: http://irep.iium.edu.my/id/eprint/13695

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