p-Adic phase transitions for countable state Potts model

The statistical mechanical models with finitely many spin values have several applications in many areas of natural science. One of the most studied models is the Potts model, which has a rich structure of physical phenomena. However, countable analog of the mentioned model has not been deeply studied yet. In the present paper, we are going to construct generalized (Formula presented.) -adic Gibbs measures (for the countable state (Formula presented.) -adic Potts model on a Cayley tree) by investigating non-linear (Formula presented.) -adic dynamical systems on the sequence spaces. The provided study offers the existence of the strong phase transition for the model.