Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI:10.1134/S0040577924060114

M. M. Rakhmatullaev, B. M. Isakov

引用次数: 0

Abstract

We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model.

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二阶 Cayley 树上 Ising-Potts 模型的平移不变吉布斯量纲

摘要我们考虑了由 Cayley 树上的三态 Ising-Potts 模型给出的混合型模型。得到了该模型在任意阶 Cayley 树上存在极限 Gibbs 量的判据。研究了二阶 Cayley 树上的平移不变吉布斯量。证明了相变的存在：在一个参数值范围内，三态 Ising-Potts 模型有一到七个吉布斯量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.