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

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26 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)165-176
Number of pages12
JournalProceedings of the Steklov Institute of Mathematics
Volume265
Issue number1
DOIs
Publication statusPublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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