Phase transition of the Potts model with three competing interactions on Cayley tree of order 3.

In this paper, we consider the Potts model with competing interactions on the Cayley tree of order three. Also we assume the state space set of the Potts model as Φ = {1,2,3,4} while it has taken as Φ = {1,2,3} in the previous studies [3, 8, 9]. we construct the Gibbs measures corresponding to the model by using Markov random field method. We calculate the critical curve such that there is a phase transition for the model. We extend the results introduced in the references [3, 8]. [ABSTRACT FROM AUTHOR]