Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree

被引：0

作者：

R. M. Khakimov

机构：

[1] Namangan State University,

来源：

Theoretical and Mathematical Physics | 2014年 / 179卷

关键词：

Cayley tree; configuration; Gibbs measure; Potts model; “solid-on-solid” model; periodic measure; translation-invariant measure;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study Potts and “solid-on-solid” models with q ≥ 2 states on the Cayley tree of order k ≥ 1. For any values of the parameter q in the Potts model and q ≤ 6 in the “solid-on-solid” model, we find sets containing all translation-invariant Gibbs measures.

引用

页码：405 / 415

页数：10

共 50 条

[1] LOCALIZATION OF TRANSLATION-INVARIANT GIBBS MEASURES FOR THE POTTS AND "SOLID-ON-SOLID" MODELS ON A CAYLEY TREE
Khakimov, R. M.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2014, 179 (01) : 405 - 415
[2] TRANSLATION-INVARIANT AND PERIODIC GIBBS MEASURES FOR THE POTTS MODEL ON A CAYLEY TREE
Khakimov, R. M.
Khaydarov, F. Kh.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2016, 189 (02) : 1651 - 1659
[3] Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree
U. A. Rozikov
R. M. Khakimov
F. Kh. Khaidarov
[J]. Theoretical and Mathematical Physics, 2018, 196 : 1043 - 1058
[4] Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree
Rozikov, U. A.
Khakimov, R. M.
Khaidarov, F. Kh.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2018, 196 (01) : 1043 - 1058
[5] Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
R. M. Khakimov
F. Kh. Khaydarov
[J]. Theoretical and Mathematical Physics, 2016, 189 : 1651 - 1659
[6] Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree
C. Külske
U. A. Rozikov
R. M. Khakimov
[J]. Journal of Statistical Physics, 2014, 156 : 189 - 200
[7] Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree
Kuelske, C.
Rozikov, U. A.
Khakimov, R. M.
[J]. JOURNAL OF STATISTICAL PHYSICS, 2014, 156 (01) : 189 - 200
[8] Extremality of translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree
Rahmatullaev, M. M.
Rasulova, M. A.
[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2021, 2021 (07):
[9] ON (κ0)-TRANSLATION-INVARIANT AND (κ0)-PERIODIC GIBBS MEASURES FOR POTTS MODEL ON CAYLEY TREE
Dekhkonov, J. D.
[J]. UFA MATHEMATICAL JOURNAL, 2022, 14 (04): : 42 - 55
[10] Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree
U. A. Rozikov
M. M. Rakhmatullaev
R. M. Khakimov
[J]. Theoretical and Mathematical Physics, 2022, 210 : 135 - 153

← 1 2 3 4 5 →