On Gibbs measures of P-adic Potts model on the cayley tree

Farruh M. Mukhamedov, Utkir A. Rozikov

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ε ℚp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ε pℕ> and p ≥ 3 (resp. q ε 22ℕ, p = 2). It is established that for p -adic Potts model at k ≥ 3 a phase transition may occur only at q ε p ℕ if p ≥ 3 and q ε 22ℕ if p = 2.

Original languageEnglish
Pages (from-to)85-99
Number of pages15
JournalIndagationes Mathematicae
Issue number1
Publication statusPublished - 2004
Externally publishedYes


  • Cayley tree
  • Gibbs measure
  • Phase transition
  • Potts model
  • p-adic field

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'On Gibbs measures of P-adic Potts model on the cayley tree'. Together they form a unique fingerprint.

Cite this