Existence of a Phase Transition for the Potts p-adic Model on the Set ℤ

Abstract

We consider the Potts model on the set ℤ in the field Qp of p-adic numbers. The range of the spin variables σ(n), \(n \in \mathbb{Z}\), in this model is \(\Phi = \left\{ {\sigma _1 ,\sigma _2 ,...,\sigma _q } \right\} \subset Q_p^{q - 1} = \underbrace {Q_p \times Q_p \times \cdot \cdot \cdot \times Q_p }_{q - 1}\). We show that there are some values q=q(p) for which phase transitions occur.