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

Farrukh Mukhamedov, Mutlay Dogan

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)25-46
Number of pages22
JournalReports on Mathematical Physics
Issue number1
Publication statusPublished - Feb 1 2015
Externally publishedYes


  • Cayley tree
  • P-adic numbers
  • P-adic quasi Gibbs measure
  • Phase transition
  • λ-model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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