This article is cited in 4 papers

The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree

Rustam M. Khakimov

Institute of Mathematics, Do’rmon Yo’li str., 29, Tashkent, 100125, Uzbekistan

Abstract: We consider fertile Hard-Core (HC) models with activity parameter $\lambda>0$ and four states on the Cayley tree of order two. It is known that there are three types of such models. In this paper for each of these models the uniqueness of the translation-invariant Gibbs measure is proved.

Keywords: Cayley tree, configuration, HC-model, Gibbs measure, translation-invariant measures.

UDC: 517.98

Received: 04.01.2015
Received in revised form: 17.02.2015
Accepted: 06.03.2015

Language: English