{"title":"Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees","authors":"N.N. Ganikhodjaev, N.M. Khatamov, U.A. Rozikov","doi":"10.1016/s0034-4877(23)00082-4","DOIUrl":null,"url":null,"abstract":"<p><span>The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set\n</span><span><math><mrow is=\"true\"><mi is=\"true\" mathvariant=\"double-struck\">Z</mi></mrow></math></span> of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several <em>q</em>-height-periodic translations invariant GGMs for <em>q</em> = 2, 3, 4.</p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"33 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-12-30","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://doi.org/10.1016/s0034-4877(23)00082-4","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
The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set
of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several q-height-periodic translations invariant GGMs for q = 2, 3, 4.
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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