Gibbs Measures for HC-Model with a Cuountable Set of Spin Values on a Cayley Tree

被引：1

作者：

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

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

Rozikov, U. A. ^{[1
,3
,4
]}

机构：

[1] VI Romanovskiy Inst Math, 9 Univ Str, Tashkent 100174, Uzbekistan

[2] Namangan State Univ, Namangan, Uzbekistan

[3] AKFA Univ, Natl Pk St, Tashkent, Uzbekistan

[4] Natl Univ Uzbekistan, 4 Univ Str, Tashkent 100174, Uzbekistan

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2023年 / 26卷 / 02期

关键词：

HC model; Configuration; Cayley tree; Gibbs measure; Boundary law; HARD-CORE MODEL; POTTS-MODEL; COUNTABLE SET; FUZZY TRANSFORMATIONS;

D O I：

10.1007/s11040-023-09453-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the HC-model with a countable set Z of spin values on a Cayley tree of order k= 2. This model is defined by a countable set of parameters (that is, the activity function ?(i) > 0, i ? Z). A functional equation is obtained that provides the consistency condition for finite-dimensional Gibbs distributions. Analyzing this equation, the following results are obtained:- Let ? = S-i ?(i). For ? = +8 there is no translation-invariant Gibbs measure (TIGM) and no two-periodic Gibbs measure (TPGM);- For ? < +8, the uniqueness of TIGM is proved;- Let ?(cr)(k) = k(k)/ (k-1)(k+1) . If 0 < ? = ?(cr), then there is exactly one TPGM that is TIGM;- For ? > ?(cr), there are exactly three TPGMs, one of which is TIGM.

引用

页数：22

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