This article is cited in 3 papers

A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree

M. M. Rahmatullaev

Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study the Potts model with $q$ states in a Cayley tree of order $k\ge2$. For the ferromagnetic Potts model, we prove the existence of a weakly periodic Gibbs measure that is not translation-invariant.

Keywords: Cayley tree, Gibbs measure, Potts model, weakly periodic Gibbs measure.

UDC: 517.98+530.1

Received: 17.11.2014

DOI: 10.17377/smzh.2015.56.515

 English version: Siberian Mathematical Journal, 2015, 56:5, 929–935

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