New class of Gibbs measures for two-state hard-core model on a Cayley tree

被引：3

作者：

Khakimov, R. M. ^{[1
,2
]}

Makhammadaliev, M. T. ^{[1
,2
]}

Haydarov, F. H. ^{[1
,3
,4
,5
]}

机构：

[1] Inst Math, 9 Univ St, Tashkent 100174, Uzbekistan

[2] Namangan State Univ, Uychi St, Namangan 716019, Uzbekistan

[3] New Uzbekistan Univ, 54 Mustaqill Ave, Tashkent 100007, Uzbekistan

[4] Cent Asian Univ, 264 Milliy Bog St, Tashkent 111221, Uzbekistan

[5] Natl Univ Uzbekistan, Univ St, Tashkent 100174, Uzbekistan

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2023年 / 26卷 / 04期

关键词：

Cayley tree; configuration; hard-core model; Gibbs measure; translation-invariant measure; alternating Gibbs measure; free energy; ISING-MODEL; POTTS-MODEL; UNIQUENESS; STATES;

D O I：

10.1142/S0219025723500248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a Hard-Core (HC) model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we show that the existence of alternative Gibbs measures which are not translation-invariant. In addition, we study free energy of the model.

引用

页数：28

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