A Dynamical System Approach to Phase Transitions for p-Adic Potts Model on the Cayley Tree of Order Two

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31 Citations (Scopus)

Abstract

In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition phenomena for the given model. Namely, using the derived recursive relations we define a one-dimensional fractional p-adic dynamical system. We show that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. In this case, there exists a strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields the existence of a quasi phase transition.

Original languageEnglish
Pages (from-to)385-406
Number of pages22
JournalReports on Mathematical Physics
Volume70
Issue number3
DOIs
Publication statusPublished - Dec 2012
Externally publishedYes

Keywords

  • P-adic numbers
  • P-adic quasi Gibbs measure
  • Phase transition
  • Potts model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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