On the uniqueness of Gibbs measures for p-adic nonhomogeneous λ-model on the Cayley tree

Murod Khamraev, Farruh Mukhamedov, Utkir Rozikov

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We consider a nearest-neighbor p-adic λ-model with spin values ±1 on a Cayley tree of order k ≥ 1. We prove for the model there is no phase transition and as well as being unique, the p-adic Gibbs measure is bounded if and only if p ≥ 3. If p = 2, then we find a condition which guarantees the nonexistence of a phase transition. Besides, the results are applied to the p-adic Ising model and we show that for the model there is a unique p-adic Gibbs measure.

Original languageEnglish
Pages (from-to)17-28
Number of pages12
JournalLetters in Mathematical Physics
Volume70
Issue number1
DOIs
Publication statusPublished - Oct 2004
Externally publishedYes

Keywords

  • Cayley tree
  • Gibbs measure
  • Ising model
  • p-adic field
  • λ-model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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