On inhomogeneous p-adic potts model on a cayley tree

Farrukh Mukhamedov, Utkir Rozikov

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


We consider a nearest-neighbor inhomogeneous p-adic Potts (with q ≥ 2 spin values) model on the Cayley tree of order k ≥ 1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p-adic) Gibbs measures of the model. We show that (i) if q ∉ pℕ then there is unique Gibbs measure for any k ≥ 1 and ∀ Jxy with |Jxy| < p -1/(p-1). (ii) For q ∈ pℕ, p ≥ 3 one can choose J xy and k ≥ l such that there exist at least two Gibbs measures which are translation-invariant.

Original languageEnglish
Pages (from-to)277-290
Number of pages14
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Issue number2
Publication statusPublished - Jun 2005
Externally publishedYes


  • Cayley tree
  • Gibbs measure
  • P-adic field
  • Potts model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics


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