This article is cited in 13 papers

Translation-invariant Gibbs measures for fertile three-state “hard core” models on a Cayley tree

R. M. Khakimov

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

Abstract: We consider fertile three-state "hard core" models with the activity parameter $\lambda>0$ on an order-three Cayley tree. It is known that there exist four types of such models: in two of them, the translation-invariant Gibbs measure is unique for $\lambda>0$, and in the other two, a value $\lambda_\mathrm{cr}$ is found such that there exist only three translation-invariant Gibbs measures for $\lambda>\lambda_\mathrm{cr}$ and a single translation-invariant Gibbs measure for $\lambda\le\lambda_\mathrm{cr}$.

Keywords: Cayley tree, configuration, hard core model, Gibbs measure, translation-invariant measure.

Received: 30.04.2014
Revised: 17.09.2014

DOI: 10.4213/tmf8700

 English version: Theoretical and Mathematical Physics, 2015, 183:3, 829–835

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