Weakly Periodic Gibbs Measures for HC-Models on Cayley Trees

被引：6

作者：

Khakimov, R. M. ^{[1
]}

机构：

[1] Namangan State Univ, Namangan, Uzbekistan

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2018年 / 59卷 / 01期

关键词：

Cayley tree; configuration; HC-model; fertile graph; Gibbs measure; weakly periodic measure; translation-invariant measure; HARD-CORE MODELS; UNIQUENESS; STATES;

D O I：

10.1134/S0037446618010160

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

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收藏

页码：147 / 156

页数：10

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