On p-adic quasi Gibbs measures for q + 1-state Potts model on the Cayley tree

Farrukh Mukhamedov

doi:10.1134/S2070046610030064

On p-adic quasi Gibbs measures for q + 1-state Potts model on the Cayley tree

Farrukh Mukhamedov

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

29 Citations (Scopus)

Abstract

In the present paper we introduce a new kind of p-adic measures, associated with q + 1-state Potts model, called p-adic quasi Gibbs measure, which is totally different from the p-adic Gibbs measure. We establish the existence of p-adic quasi Gibbs measures for the model on a Cayley tree. If q is divisible by p, then we prove the occurrence of a strong phase transition. If q and p are relatively prime, then there is a quasi phase transition. These results are totally different from the results of [F. M. Mukhamedov and U. A. Rozikov, Indag. Math. N. S.

Original language	English
Pages (from-to)	241-251
Number of pages	11
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume	2
Issue number	3
DOIs	https://doi.org/10.1134/S2070046610030064
Publication status	Published - Sept 1 2010
Externally published	Yes

Keywords

Potts model
p-adic numbers
p-adic quasi Gibbs measure
phase transition

ASJC Scopus subject areas

General Mathematics

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10.1134/S2070046610030064

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abstract = "In the present paper we introduce a new kind of p-adic measures, associated with q + 1-state Potts model, called p-adic quasi Gibbs measure, which is totally different from the p-adic Gibbs measure. We establish the existence of p-adic quasi Gibbs measures for the model on a Cayley tree. If q is divisible by p, then we prove the occurrence of a strong phase transition. If q and p are relatively prime, then there is a quasi phase transition. These results are totally different from the results of [F. M. Mukhamedov and U. A. Rozikov, Indag. Math. N. S.",

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N2 - In the present paper we introduce a new kind of p-adic measures, associated with q + 1-state Potts model, called p-adic quasi Gibbs measure, which is totally different from the p-adic Gibbs measure. We establish the existence of p-adic quasi Gibbs measures for the model on a Cayley tree. If q is divisible by p, then we prove the occurrence of a strong phase transition. If q and p are relatively prime, then there is a quasi phase transition. These results are totally different from the results of [F. M. Mukhamedov and U. A. Rozikov, Indag. Math. N. S.

AB - In the present paper we introduce a new kind of p-adic measures, associated with q + 1-state Potts model, called p-adic quasi Gibbs measure, which is totally different from the p-adic Gibbs measure. We establish the existence of p-adic quasi Gibbs measures for the model on a Cayley tree. If q is divisible by p, then we prove the occurrence of a strong phase transition. If q and p are relatively prime, then there is a quasi phase transition. These results are totally different from the results of [F. M. Mukhamedov and U. A. Rozikov, Indag. Math. N. S.

KW - Potts model

KW - p-adic numbers

KW - p-adic quasi Gibbs measure

KW - phase transition

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On p-adic quasi Gibbs measures for q + 1-state Potts model on the Cayley tree

Abstract

Keywords

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