This article is cited in 3 papers

Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree

R. M. Khakimov

Namangam State University

Abstract: We study Potts and “solid-on-solid” models with $q\ge2$ states on the Cayley tree of order $k\ge1$. For any values of the parameter $q$ in the Potts model and $q\le6$ in the “solid-on-solid” model, we find sets containing all translation-invariant Gibbs measures.

Keywords: Cayley tree, configuration, Gibbs measure, Potts model, “solid-on-solid” model, periodic measure, translation-invariant measure.

Received: 02.10.2013

DOI: 10.4213/tmf8599

 English version: Theoretical and Mathematical Physics, 2014, 179:1, 405–415

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