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On P-Adic lambda-model on the cayley tree II: Phase transitions

Mukhamedov, Farrukh and Dogan, Mutlay (2015) On P-Adic lambda-model on the cayley tree II: Phase transitions. Reports on Mathematical Physics, 75 (1). pp. 25-46. ISSN 00344877

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In the present paper, we consider the p-adic λ-model on the Cayley tree of order two. It is considered generalized p-adic quasi Gibbs measure depending on a parameter ρ ∈ p, for the λ-model. In the p-adic setting there are several kinds of phase transitions such as storing phase transition, phase transition in terms of the generalized p-adic quasi Gibbs measures. In the paper, we consider two regimes with respect to the parameter ρ. The existence of generalized p-adic Gibbs measures in both regimes is proved. We prove the existence of the phase transition for the p-adic λ model on the Cayley tree of order two in the first regime. It turns out that in the second regime, we are able to establish the strong phase transition for a class of λ-models on the same tree. To prove the main results, we employ the methods of p-adic analysis, and therefore, our results are not valid in the real setting.

Item Type: Article (Journal)
Additional Information: 5537/42131
Uncontrolled Keywords: Cayley tree; P-adic numbers; P-adic quasi Gibbs measure; Phase transition; λ-model
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 27 Feb 2015 15:46
Last Modified: 10 Nov 2016 10:45
URI: http://irep.iium.edu.my/id/eprint/42131

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