Translation-invariant and weakly periodic Gibbs measures for HC-models on a Cayley tree

2015/12/13 by Rustam Khakimov, Khakimov, Rustam
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1601.02558

openalex publication_date 2015/12/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper is studied HC-models on a Cayley tree. two states HC-model on a Cayley tree and Under some conditions on parameters of the two state HC-model we prove existence exactly two of the weakly periodic (non periodic) Gibbs measures. Furthermore, it considered translation-invariant Gibbs measures for fertile four state HC-models and for one of them it proved the non-uniqueness of the translation-invariant Gibbs measure.

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