Fixed points and phase transitions for the p-adic Potts model with an external field

In this paper, we investigate a two-variable [Formula: see text]-adic dynamical system associated with the Potts model with an external field on the Cayley tree of order two. We analyze the fixed points of the corresponding operator and identify four saddle points. Based on these fixed points, we construct four new translation-invariant [Formula: see text]-adic quasi Gibbs measures for the Potts model. Furthermore, we establish new sufficient conditions for the existence of a phase transition in the model by examining the boundedness of these measures.