This article is cited in 8 papers

Weakly periodic Gibbs measures for HC-models on Cayley trees

R. M. Khakimov

Namangan State University, Namangan, Uzbekistan

Abstract: We study hard-core (HC) models on Cayley trees. Given a $2$-state HC-model, we prove that exactly two weakly periodic (aperiodic) Gibbs measures exist under certain conditions on the parameters. Moreover, we consider fertile $4$-state HC-models with the activity parameter $\lambda>0$. The three types of these models are known to exist. For one of the models we show that the translationinvariant Gibbs measure is not unique.

Keywords: Cayley tree, configuration, HC-model, fertile graph, Gibbs measure, weakly periodic measure, translation-invariant measure.

UDC: 517.98

Received: 07.12.2015

DOI: 10.17377/smzh.2018.59.116

 English version: Siberian Mathematical Journal, 2018, 59:1, 147–156

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