On Gibbs measures of P-adic Potts model on the cayley tree

Farruh M. Mukhamedov; Utkir A. Rozikov

doi:10.1016/S0019-3577(04)90007-9

On Gibbs measures of P-adic Potts model on the cayley tree

Farruh M. Mukhamedov, Utkir A. Rozikov

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

Abstract

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ε ℚ_p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ε pℕ> and p ≥ 3 (resp. q ε 2²ℕ, p = 2). It is established that for p -adic Potts model at k ≥ 3 a phase transition may occur only at q ε p ℕ if p ≥ 3 and q ε 2²ℕ if p = 2.

Original language	English
Pages (from-to)	85-99
Number of pages	15
Journal	Indagationes Mathematicae
Volume	15
Issue number	1
DOIs	https://doi.org/10.1016/S0019-3577(04)90007-9
Publication status	Published - 2004
Externally published	Yes

Keywords

Cayley tree
Gibbs measure
Phase transition
Potts model
p-adic field

ASJC Scopus subject areas

Mathematics(all)

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10.1016/S0019-3577(04)90007-9

Cite this

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title = "On Gibbs measures of P-adic Potts model on the cayley tree",

abstract = "We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ε ℚp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ε pℕ> and p ≥ 3 (resp. q ε 22ℕ, p = 2). It is established that for p -adic Potts model at k ≥ 3 a phase transition may occur only at q ε p ℕ if p ≥ 3 and q ε 22ℕ if p = 2.",

keywords = "Cayley tree, Gibbs measure, Phase transition, Potts model, p-adic field",

author = "Mukhamedov, {Farruh M.} and Rozikov, {Utkir A.}",

note = "Funding Information: This work was done within the scheme of Mathematical fellowship at the Ab-dus Salam International Center for Theoretical Physics (ICTP) and the authors thank ICTP and IMU/CDE - program for providing financial support and all facilities. The authors acknowledge with gratitude to Professors I.V.Volovich and A.Yu.Khrennikov for the helpful comments and discussions. The authors are also grateful to the referee for useful suggestions.",

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doi = "10.1016/S0019-3577(04)90007-9",

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volume = "15",

pages = "85--99",

journal = "Indagationes Mathematicae",

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publisher = "Elsevier",

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TY - JOUR

T1 - On Gibbs measures of P-adic Potts model on the cayley tree

AU - Mukhamedov, Farruh M.

AU - Rozikov, Utkir A.

N1 - Funding Information: This work was done within the scheme of Mathematical fellowship at the Ab-dus Salam International Center for Theoretical Physics (ICTP) and the authors thank ICTP and IMU/CDE - program for providing financial support and all facilities. The authors acknowledge with gratitude to Professors I.V.Volovich and A.Yu.Khrennikov for the helpful comments and discussions. The authors are also grateful to the referee for useful suggestions.

PY - 2004

Y1 - 2004

N2 - We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ε ℚp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ε pℕ> and p ≥ 3 (resp. q ε 22ℕ, p = 2). It is established that for p -adic Potts model at k ≥ 3 a phase transition may occur only at q ε p ℕ if p ≥ 3 and q ε 22ℕ if p = 2.

AB - We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ε ℚp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ε pℕ> and p ≥ 3 (resp. q ε 22ℕ, p = 2). It is established that for p -adic Potts model at k ≥ 3 a phase transition may occur only at q ε p ℕ if p ≥ 3 and q ε 22ℕ if p = 2.

KW - Cayley tree

KW - Gibbs measure

KW - Phase transition

KW - Potts model

KW - p-adic field

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DO - 10.1016/S0019-3577(04)90007-9

M3 - Article

AN - SCOPUS:4344616812

SN - 0019-3577

VL - 15

SP - 85

EP - 99

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

On Gibbs measures of P-adic Potts model on the cayley tree

Abstract

Keywords

ASJC Scopus subject areas

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