This article is cited in 7 papers

$p$-Adic Gibbs measures for the hard core model with three states on the Cayley tree

O. N. Khakimov

Institute for Mathematics and Information Technologies, Academy of Sciences of Uzbekistan Republic, Tashkent, Uzbekistan

Abstract: We study $p$-adic hard core models with three states on the Cayley tree. It is known that there are four types of such models. We find conditions that must be imposed on the order $k$ of the Cayley tree and on the prime $p$ for a translation-invariant $p$-adic Gibbs measure to exist.

Keywords: Cayley tree, configuration, Gibbs measure, hard core $G$-model, translation-invariant measure, $p$-adic number.

Received: 27.03.2013

DOI: 10.4213/tmf8603

 English version: Theoretical and Mathematical Physics, 2013, 177:1, 1339–1351

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