Weakly Periodic Gibbs Measures for HC-Models on Cayley Trees

Сибирский математический журнал

R. M. Khakimov¹ 

[1] Namangan State University

关键词: Cayley tree;    configuration;    HC-model;    fertile graph;    Gibbs measure;    weakly periodic measure;    translation-invariant measure;   

DOI  :  10.1134/S0037446618010160

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 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 λ > 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.

【 授权许可】

CC BY