This article is cited in 7 papers

The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model

U. A. Rozikov^a, R. M. Khakimov<sup>b

a</sup> Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
^b Namangan State University, Namangan, Uzbekistan

Abstract: We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant.

Keywords: Cayley tree, configuration, hard-core model, Gibbs measure, periodic measure, weakly periodic measure.

Received: 20.02.2012

DOI: 10.4213/tmf6966

 English version: Theoretical and Mathematical Physics, 2012, 173:1, 1377–1386

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