Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree

F. M. Mukhamedov, M. Kh Saburov, O. Kh Khakimov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, “phase transition” means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case.

Original languageEnglish
Pages (from-to)583-602
Number of pages20
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume187
Issue number1
DOIs
Publication statusPublished - Apr 1 2016
Externally publishedYes

Keywords

  • Cayley tree
  • Ising–Vannimenus model
  • dynamical system
  • p-adic Gibbs measure
  • p-adic numbers
  • phase transition

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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