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

• Main Authors: Mukhamedov, Farrukh, Dogan, Mutlay
• 格式: Article
• 语言: English
• 出版: Elsevier 2015
• 主题: QA Mathematics; QC Physics
• 在线阅读: http://irep.iium.edu.my/42131/1/mfmd-RMP%282015%29.pdf; http://irep.iium.edu.my/42131/; http://www.journals.elsevier.com/reports-on-mathematical-physics/

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.