Phase transitions for p-adic Potts model on the Cayley tree of order three

Farrukh Mukhamedov, Hasan Akin

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


In the present paper, we study a phase transition problem for the q-state p-adic Potts model over the Cayley tree of order three. We consider a more general notion of p-adic Gibbs measure which depends on parameter ρ∈Qp. Such a measure is called generalized p-adic quasi Gibbs measure. When ρ equals the p-adic exponent, then it coincides with the p-adic Gibbs measure. When ρ = p, then it coincides with the p-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of |ρ|p. Namely, in the first regime, one takes ρ = exp p(J) for some J∈Qp, in the second one |ρ| p < 1. In each regime, we first find conditions for the existence of generalized p-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when |ρ|p,|q|p ≤ p-2 we prove the existence of a quasi phase transition. It turns out that if and , then one finds the existence of the strong phase transition.

Original languageEnglish
Article numberP07014
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number7
Publication statusPublished - Jul 2013
Externally publishedYes


  • classical phase transitions (theory)
  • rigorous results in statistical mechanics

ASJC Scopus subject areas

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


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