On phase transitions for p-adic potts model with competing interactions on a cayley tree

F. M. Mukhamedov; U. A. Rozikov; J. F.F. Mendes

doi:10.1063/1.2193118

On phase transitions for p-adic potts model with competing interactions on a cayley tree

F. M. Mukhamedov, U. A. Rozikov, J. F.F. Mendes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

11 Citations (Scopus)

Abstract

In the paper we consider three state p-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the p-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if p = 3 for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a p-adic context. Namely, if p ≠ 3 then there is only a unique Gibbs measure the model.

Original language	English
Title of host publication	P-ADIC MATHEMATICAL PHYSICS
Subtitle of host publication	2nd International Conference on p-Adic Mathematical Physics
Pages	140-150
Number of pages	11
DOIs	https://doi.org/10.1063/1.2193118
Publication status	Published - Mar 29 2006
Externally published	Yes
Event	2nd International Conference on p-Adic Mathematical Physics - Belgrade Duration: Sept 15 2005 → Sept 21 2005

Publication series

Name	AIP Conference Proceedings
Volume	826
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2nd International Conference on p-Adic Mathematical Physics
City	Belgrade
Period	9/15/05 → 9/21/05

Keywords

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

ASJC Scopus subject areas

Ecology, Evolution, Behavior and Systematics
Ecology
Plant Science
General Physics and Astronomy
Nature and Landscape Conservation

Access to Document

10.1063/1.2193118

Cite this

On phase transitions for p-adic potts model with competing interactions on a cayley tree. / Mukhamedov, F. M.; Rozikov, U. A.; Mendes, J. F.F.
P-ADIC MATHEMATICAL PHYSICS: 2nd International Conference on p-Adic Mathematical Physics. 2006. p. 140-150 (AIP Conference Proceedings; Vol. 826).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Mukhamedov, FM, Rozikov, UA & Mendes, JFF 2006, On phase transitions for p-adic potts model with competing interactions on a cayley tree. in P-ADIC MATHEMATICAL PHYSICS: 2nd International Conference on p-Adic Mathematical Physics. AIP Conference Proceedings, vol. 826, pp. 140-150, 2nd International Conference on p-Adic Mathematical Physics, Belgrade, 9/15/05. https://doi.org/10.1063/1.2193118

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AB - In the paper we consider three state p-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the p-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if p = 3 for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a p-adic context. Namely, if p ≠ 3 then there is only a unique Gibbs measure the model.

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KW - Phase transition

KW - Potts model

KW - Uniqueness

KW - p-adic field

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On phase transitions for p-adic potts model with competing interactions on a cayley tree

Abstract

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Keywords

ASJC Scopus subject areas

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