{"title":"Weakly periodic gibbs measures for the HC model with a countable set of spin values","authors":"","doi":"10.1016/S0034-4877(24)00057-0","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study the weakly periodic (nonperiodic) Gibbs measures for the Hard Core (HC) model with a countable set ℤ of spin values and with a countable set of parameters <em>λ<sub>i</sub> ></em> 0, <em>i</em> ∈ ℤ, on a Cayley tree of order <em>k</em> ≥ 2. For the considered model in the case ∑<em><sub>i</sub></em> λ<em><sub>i</sub></em> < +∞, a complete description of weakly periodic Gibbs measures is obtained for any normal divisor of index two and in the case ∑<em><sub>i</sub></em>; λ<em><sub>i</sub></em> = +∞, it is shown that there is no weakly periodic Gibbs measure. Moreover, in the case of a normal divisor of index four the uniqueness conditions for weakly periodic Gibbs measures are found. Further, under certain conditions an exact critical value is found that ensures the existence of weakly periodic Gibbs measures.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000570","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the weakly periodic (nonperiodic) Gibbs measures for the Hard Core (HC) model with a countable set ℤ of spin values and with a countable set of parameters λi > 0, i ∈ ℤ, on a Cayley tree of order k ≥ 2. For the considered model in the case ∑i λi < +∞, a complete description of weakly periodic Gibbs measures is obtained for any normal divisor of index two and in the case ∑i; λi = +∞, it is shown that there is no weakly periodic Gibbs measure. Moreover, in the case of a normal divisor of index four the uniqueness conditions for weakly periodic Gibbs measures are found. Further, under certain conditions an exact critical value is found that ensures the existence of weakly periodic Gibbs measures.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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