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 language | English |
---|---|
Pages (from-to) | 385-406 |
Number of pages | 22 |
Journal | Reports on Mathematical Physics |
Volume | 70 |
Issue number | 3 |
DOIs | |
Publication status | Published - Dec 2012 |
Externally published | Yes |
Keywords
- P-adic numbers
- P-adic quasi Gibbs measure
- Phase transition
- Potts model
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics