Periodic Gibbs measures for three-state hard-core models in the case Wand

2020/07/29 by Р. М. Хакимов, Khakimov, R. M., K. O. Umirzakova +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graph theory and applications #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2007.14611

openalex publication_date 2020/07/29 · openalex created_date 2023/08/22 · openalex updated_date 2026/07/28

Abstract

We consider fertile three-state Hard-Core (HC) models with the activity parameter λ>0 on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. These models arise as simple examples of loss networks with nearest-neighbor exclusion. In the case wand on a Cayley tree of order k≥2, exact critical values λ>0 are found for which two-periodic Gibbs measures are not unique. Moreover, we study the extremality of the existing two-periodic Gibbs measures on a Cayley tree of order two.

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