Phase diagram of the Potts Model with competing interactions

Abstract. We study the phase diagram for the Potts Model on a Cayley tree with competing nearest-neighbor interaction J_1 and next-nearest-neighbor interactions J_2 and J_3. To perform this study, an iterative scheme similar to that appearing in real space renormalizatiort group frameworks is established.The phase digram contains a modulated phase as found for similar models on periodic lattices, and also new phase ,namely, antiferromagnetic phase