A p-Adic Generalized Gibbs Measure for the Ising Model on a Cayley Tree

被引：12

作者：

Rahmatullaev, M. M. ^{[1
,2
]}

Khakimov, O. N. ^{[2
]}

Tukhtaboev, A. M. ^{[3
]}

机构：

[1] Namangan State Univ, Namangan, Uzbekistan

[2] Inst Math, Tashkent, Uzbekistan

[3] Namangan Construct Inst, Namangan, Uzbekistan

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2019年 / 201卷 / 01期

关键词：

p-adic number; Ising model; Gibbs measure; phase transition; STATE POTTS-MODEL; HARD-CORE MODEL; LAMBDA-MODEL; UNIQUENESS;

D O I：

10.1134/S004057791910009X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a p-adic Ising model on the Cayley tree of order k >= 2. We completely describe all p-adic-translation-invariant generalized Gibbs measures for k = 3. Moreover, we show the existence of a phase transition for the p-adic Ising model for any k >= 3 if p equivalent to 1 (mod 4).

引用

页码：1521 / 1530

页数：10

共 29 条

[1] A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree [J].

Akin, H. ;

Rozikov, U. A. ;

Temir, S. .

JOURNAL OF STATISTICAL PHYSICS, 2011, 142 (02) :314-321

[2] A RANDOM-WALK ON P-ADICS - THE GENERATOR AND ITS SPECTRUM [J].

ALBEVERIO, S ;

KARWOWSKI, W .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 53 (01) :1-22

[3]

[Anonymous], 1997, Non-Archimedean Analysis, Quantum Paradoxes

[4] ON THE PURITY OF THE LIMITING GIBBS STATE FOR THE ISING-MODEL ON THE BETHE LATTICE [J].

BLEHER, PM ;

RUIZ, J ;

ZAGREBNOV, VA .

JOURNAL OF STATISTICAL PHYSICS, 1995, 79 (1-2) :473-482

[5]

Gandolfo D, 2012, MARKOV PROCESS RELAT, V18, P701

[6]

Ganikhodzhaev N. N., 1998, Uzbek. Mat. J., V4, P23

[7]

Georgii HO, 1988, DEGRUYTER STUD MATH, V9

[8] On a generalized p-adic Gibbs measure for Ising model on trees [J].

Khakimov O.N. .

P-Adic Numbers, Ultrametric Analysis, and Applications, 2014, 6 (3) :207-217

[9] On p-adic Gibbs measures for Ising model with four competing interactions [J].

Khakimov O.N. .

P-Adic Numbers, Ultrametric Analysis, and Applications, 2013, 5 (3) :194-203

[10] p-ADIC GIBBS QUASIMEASURES FOR THE VANNIMENUS MODEL ON A CAYLEY TREE [J].

Khakimov, O. N. .

THEORETICAL AND MATHEMATICAL PHYSICS, 2014, 179 (01) :395-404

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