On p-adic Ising-Vannimenus model on an arbitrary order Cayley tree

Farrukh Mukhamedov, Mansoor Saburov, Otabek Khakimov

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


In this paper, we continue an investigation of the p-adic Ising-Vannimenus model on the Cayley tree of an arbitrary order k(k ≥ 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multi-dimensional p-adic system of equations. We are also able to show the uniqueness of translation-invariant p-adic Gibbs measure. Finally, it is established the existence of the phase transition for the Ising-Vannimenus model depending on the order k of the Cayley tree and the prime p. Note that the methods used in the paper are not valid in the real setting, since all of them are based on p-adic analysis and p-adic probability measures.

Original languageEnglish
Article numberP05032
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number5
Publication statusPublished - May 27 2015
Externally publishedYes


  • phase diagrams (theory)
  • solvable lattice models

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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