Cayley树上不可数自旋值集模型Gibbs测度唯一性的新条件

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-20 DOI:10.1007/s11040-021-09404-3

F. H. Haydarov

{"title":"Cayley树上不可数自旋值集模型Gibbs测度唯一性的新条件","authors":"F. H. Haydarov","doi":"10.1007/s11040-021-09404-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we consider a model with nearest-neighbor interactions with spin space [0, 1] on Cayley trees of order <i>k</i> ⩾ 2. In Yu et al. (2013), a sufficient condition of uniqueness for the splitting Gibbs measure of the model is given. We investigate the sufficient condition of uniqueness and obtain better estimates.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-021-09404-3.pdf","citationCount":"1","resultStr":"{\"title\":\"New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree\",\"authors\":\"F. H. Haydarov\",\"doi\":\"10.1007/s11040-021-09404-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we consider a model with nearest-neighbor interactions with spin space [0, 1] on Cayley trees of order <i>k</i> ⩾ 2. In Yu et al. (2013), a sufficient condition of uniqueness for the splitting Gibbs measure of the model is given. We investigate the sufficient condition of uniqueness and obtain better estimates.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11040-021-09404-3.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-021-09404-3\",\"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/s11040-021-09404-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

在本文中，我们考虑在k阶或小于2的Cayley树上具有与自旋空间[0,1]的最近邻相互作用的模型。Yu et al.(2013)给出了模型分裂Gibbs测度的唯一性的充分条件。我们研究了唯一性的充分条件，得到了较好的估计。

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

New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree

In this paper we consider a model with nearest-neighbor interactions with spin space [0, 1] on Cayley trees of order k ⩾ 2. In Yu et al. (2013), a sufficient condition of uniqueness for the splitting Gibbs measure of the model is given. We investigate the sufficient condition of uniqueness and obtain better estimates.

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： 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. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.