## Abstract

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∈Q_{p}. 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∈Q_{p}, 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 language | English |
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Article number | P07014 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2013 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2013 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

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