凯利树上具有化学势的魔杖情况下 HC 布朗-卡佩尔模型的周期吉布斯量及其极端性

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010085

N. M. Khatamov

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引用次数: 0

摘要

摘要我们研究了在万德图情况下具有化学势的 HC-Blume-Capel 模型在 Cayley 树上的周期性吉布斯量，该化学势的参数是 \(\theta,\eta)\。我们证明在这种情况下，对于 \(\theta^3\le\eta\) 存在精确的三个周期性吉布斯量，它们都是平移不变的，而对于 \(\theta^3>\eta\) 存在精确的三个周期性吉布斯量，其中一个是平移不变的。

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Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree

Abstract

Periodic Gibbs measures for the HC-Blume–Capel model with a chemical potential with parameters \((\theta,\eta)\) on a Cayley tree in the case of a wand graph are studied. We prove that in this case for \(\theta^3\le\eta\) there exist precisely three periodic Gibbs measures, all of which are translation-invariant, while for \(\theta^3>\eta\) there exist precisely three periodic Gibbs measures, one of which is translation-invari The (non)extremality of these measures is also studied.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.