## 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 |
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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