{"title":"k阶Cayley树上Ising模型的一些非周期p进广义Gibbs测度","authors":"Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev","doi":"10.1007/s11040-023-09465-6","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, we consider a <i>p</i>-adic Ising model on a Cayley tree. The existence of non-periodic <i>p</i>-adic generalized Gibbs measures of this model is investigated. In particular, we construct <i>p</i>-adic analogue of the Bleher–Ganikhodjaev construction and generalize some constructive methods. Moreover, the boundedness of obtained measures are established, which yields the occurrence of a phase transition.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k\",\"authors\":\"Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev\",\"doi\":\"10.1007/s11040-023-09465-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present paper, we consider a <i>p</i>-adic Ising model on a Cayley tree. The existence of non-periodic <i>p</i>-adic generalized Gibbs measures of this model is investigated. In particular, we construct <i>p</i>-adic analogue of the Bleher–Ganikhodjaev construction and generalize some constructive methods. Moreover, the boundedness of obtained measures are established, which yields the occurrence of a phase transition.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-023-09465-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-023-09465-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k
In the present paper, we consider a p-adic Ising model on a Cayley tree. The existence of non-periodic p-adic generalized Gibbs measures of this model is investigated. In particular, we construct p-adic analogue of the Bleher–Ganikhodjaev construction and generalize some constructive methods. Moreover, the boundedness of obtained measures are established, which yields the occurrence of a phase transition.
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MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process.
The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed.
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