具有可数自旋值集的HC模型:不可数吉布斯测度集

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Reviews in Mathematical Physics Pub Date : 2022-06-07 DOI:10.1142/S0129055X22500398

U. Rozikov, F. Haydarov

{"title":"具有可数自旋值集的HC模型:不可数吉布斯测度集","authors":"U. Rozikov, F. Haydarov","doi":"10.1142/S0129055X22500398","DOIUrl":null,"url":null,"abstract":"We consider a hard core (HC) model with a countable set $\\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\\lambda_{i}>0, i \\in \\mathbb{Z}\\setminus\\{0\\}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A HC model with countable set of spin values: uncountable set of Gibbs measures\",\"authors\":\"U. Rozikov, F. Haydarov\",\"doi\":\"10.1142/S0129055X22500398\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a hard core (HC) model with a countable set $\\\\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\\\\lambda_{i}>0, i \\\\in \\\\mathbb{Z}\\\\setminus\\\\{0\\\\}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.\",\"PeriodicalId\":54483,\"journal\":{\"name\":\"Reviews in Mathematical Physics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reviews in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/S0129055X22500398\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reviews in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/S0129055X22500398","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 2

摘要

我们考虑了一个具有Cayley树上自旋值的可数集$\mathbb｛Z｝$的硬核（HC）模型。该模型由一组可计数的参数$\lambda_｛i｝>0，i\in\mathbb｛Z｝\setminus\｛0\｝$定义。对于所有可能的参数值，我们给出了由描述有限维测度一致性条件的函数生成的动力系统的极限点。此外，我们还证明了给定模型的每个周期吉布斯测度要么是平移不变量，要么是周期为二的周期吉布斯测度。此外，我们为这个HC模型构造了不可计数的吉布斯测度集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A HC model with countable set of spin values: uncountable set of Gibbs measures

We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Reviews in Mathematical Physics 物理-物理：数学物理

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.