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In this paper, we consider the Potts model with competing interactions on the Cayley tree of order three. We give the Potts model on the Cayley tree and its recursion relation. We construct the Gibbs states 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 show that there are phase transition of the model for some given parameters. We extend the results obtained by Akin and Temir (Condensed Matt. Phys. 14, 23003 (2011)).

On Gibbs Measures of the Potts Model with Three Competing Interactions on Cayley Tree of Order 3