A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree

被引：23

作者：

Rozikov, UA ^{[1
]}

机构：

[1] Inst Math, Tashkent 700125, Uzbekistan

来源：

JOURNAL OF STATISTICAL PHYSICS | 2006年 / 122卷 / 02期

关键词：

Cayley tree; configuration; Ising model; ground state; Gibbs measure;

D O I：

10.1007/s10955-005-8029-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the Ising model with (competing) two-step interactions and spin values +/- 1, on a Cayley tree of order k >= 1. We constructively describe groundstates and verify the Peierls condition for the model. We define notion of a contour for the model on the Cayley tree. Using a contour argument we show the existence of two different Gibbs measures.

引用

页码：217 / 235

页数：19

共 50 条

[41] On periodic Gibbs measures of the Ising model corresponding to new subgroups of the group representation of a Cayley tree
F. H. Haydarov
R. A. Ilyasova
Theoretical and Mathematical Physics, 2022, 210 : 261 - 274
[42] THE p-ADIC ISING MODEL IN AN EXTERNAL FIELD ON A CAYLEY TREE: PERIODIC GIBBS MEASURES
Mukhamedov, F. M.
Rahmatullaev, M. M.
Tukhtabaev, A. M.
Mamadjonov, R.
THEORETICAL AND MATHEMATICAL PHYSICS, 2023, 216 (02) : 1238 - 1253
[43] ON PERIODIC GIBBS MEASURES OF THE ISING MODEL CORRESPONDING TO NEW SUBGROUPS OF THE GROUP REPRESENTATION OF A CAYLEY TREE
Haydarov, F. H.
Ilyasova, R. A.
THEORETICAL AND MATHEMATICAL PHYSICS, 2022, 210 (02) : 261 - 274
[44] Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree
C. Külske
U. A. Rozikov
R. M. Khakimov
Journal of Statistical Physics, 2014, 156 : 189 - 200
[45] Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree
Kuelske, C.
Rozikov, U. A.
Khakimov, R. M.
JOURNAL OF STATISTICAL PHYSICS, 2014, 156 (01) : 189 - 200
[46] 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
[47] Periodic Gibbs measures for the Potts model on the Cayley tree
Rozikov, U. A.
Khakimov, R. M.
THEORETICAL AND MATHEMATICAL PHYSICS, 2013, 175 (02) : 699 - 709
[48] GIBBS MEASURES FOR A GENERALIZED POTTS MODEL WITH THE INTERACTION RADIUS TWO ON A CAYLEY TREE
Hatamov, N. M.
Madgoziev, G. T.
THEORETICAL AND MATHEMATICAL PHYSICS, 2015, 183 (03) : 836 - 845
[49] Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree
N. M. Hatamov
G. T. Madgoziev
Theoretical and Mathematical Physics, 2015, 183 : 836 - 845
[50] On Gibbs Measures of the Potts Model with Three Competing Interactions on Cayley Tree of Order 3
Akin, H.
Saygili, H.
ACTA PHYSICA POLONICA A, 2016, 129 (04) : 845 - 848

← 1 2 3 4 5 →