This article is cited in 1 paper

A $p$-adic hard-core model with three states on a Cayley tree

O. N. Khakimov

Institute of Mathematics, Tashkent, Uzbekistan

Abstract: We examine the $p$-adic hard-core model with three states on a Cayley tree. Translationinvariant and periodic $p$-adic Gibbs measures are studied for the hard-core model for $k=2$. We prove that every $p$-adic Gibbs measure is bounded for $p\ne2$. We show in particular that there is no strong phased transition for a hard-core model on a Cayley tree of order $k$.

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

UDC: 517.98+530.1

Received: 14.09.2015

DOI: 10.17377/smzh.2016.57.414

 English version: Siberian Mathematical Journal, 2016, 57:4, 726–734

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