GRADIENT GIBBS MEASURES OF AN SOS MODEL ON CAYLEY TREES: 4-PERIODIC BOUNDARY LAWS

被引：0

作者：

Haydarov, F. H. ^{[1
,2
]}

Rozikov, U. A. ^{[1
,2
,3
]}

机构：

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

[2] AKFA Univ, 264 Milliy Bog St, Tashkent 111221, Uzbekistan

[3] V I Romanovskiy Inst Math, 9 Univ Str, Tashkent 100174, Uzbekistan

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2022年 / 90卷 / 01期

关键词：

SOS model; configuration; Cayley tree; Gibbs measure; gradient Gibbs measures; boundary law; COEXISTENCE;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

For the SOS (solid-on-solid) model (with an external field) with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (a function defined on vertices of Cayley tree) satisfying an infinite system of functional equations. We give several concrete GGMs which correspond to periodic boundary laws.

引用

页码：81 / 101

页数：21

共 16 条

[1]

[Anonymous], 2011, De Gruyter Studies in Mathematics

[2] Phase coexistence of gradient Gibbs states [J].

Biskup, Marek ;

Kotecky, Roman .

PROBABILITY THEORY AND RELATED FIELDS, 2007, 139 (1-2) :1-39

[3] Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields [J].

Bissacot, Rodrigo ;

Endo, Eric Ossami ;

van Enter, Aernout C. D. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (12) :4126-4138

[4] On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field [J].

Bogachev, Leonid, V ;

Rozikov, Utkir A. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2019,

[5] Gradient Gibbs measures for the SOS model with integer spin values on a Cayley tree [J].

Botirov, G., I ;

Haydarov, F. H. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2020, 2020 (09)

[6]

Friedli S., 2018, Statistical mechanics of lattice systems

[7] Motion by mean curvature from the Ginzburg-Landau del phi interface model [J].

Funaki, T ;

Spohn, H .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 185 (01) :1-36

[8]

Henning F, 2022, Arxiv, DOI arXiv:2102.11899

[9] COEXISTENCE OF LOCALIZED GIBBS MEASURES AND DELOCALIZED GRADIENT GIBBS MEASURES ON TREES [J].

Henning, Florian ;

Kulske, Christof .

ANNALS OF APPLIED PROBABILITY, 2021, 31 (05) :2284-2310

[10] Gradient Gibbs measures for the SOS model with countable values on a Cayley tree [J].

Henning, Florian ;

Kuelske, Christof ;

Le Ny, Arnaud ;

Rozikov, Utkir A. .

ELECTRONIC JOURNAL OF PROBABILITY, 2019, 24

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