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

共 50 条

[21] A p-adic hard-core model with three states on a Cayley tree
Khakimov, O. N.
SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (04) : 726 - 734
[22] A p-adic hard-core model with three states on a Cayley tree
O. N. Khakimov
Siberian Mathematical Journal, 2016, 57 : 726 - 734
[23] Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model
Khakimov, R. M.
Makhammadaliev, M. T.
THEORETICAL AND MATHEMATICAL PHYSICS, 2020, 204 (02) : 1059 - 1078
[24] Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model
R. M. Khakimov
M. T. Makhammadaliev
Theoretical and Mathematical Physics, 2020, 204 : 1059 - 1078
[25] A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree
H. Akin
U. A. Rozikov
S. Temir
Journal of Statistical Physics, 2011, 142 : 314 - 321
[26] New weakly periodic Gibbs measures of Ising model on Cayley tree
Rakhmatullaev M.M.
Russian Mathematics, 2015, 59 (11) : 45 - 53
[27] A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree
Akin, H.
Rozikov, U. A.
Temir, S.
JOURNAL OF STATISTICAL PHYSICS, 2011, 142 (02) : 314 - 321
[28] Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand
Khakimov, Rustamjon
Umirzakova, Kamola
JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2024, 20 (01) : 66 - 81
[29] Periodic Gibbs measures for the Potts model on the Cayley tree
U. A. Rozikov
R. M. Khakimov
Theoretical and Mathematical Physics, 2013, 175 : 699 - 709
[30] CONSTRUCTIVE GIBBS MEASURES FOR THE ISING MODEL ON THE CAYLEY TREE
Rahmatullaev, Muzaffar m.
Burxonova, Zulxumor a.
REPORTS ON MATHEMATICAL PHYSICS, 2024, 93 (03) : 361 - 370

← 1 2 3 4 5 →