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We have found an exact phase diagram of the Potts model with next nearestneighbor interactions on the Bethe lattice of order two. The diagram consistsof five phases: ferromagnetic, paramagnetic, modulated, antiphase andparamodulated, all meeting at the Lifshitz point i.e. $p=1/3$. We report on anew phase which we denote as paramodulated, found at low temperatures andcharacterized by 2-periodic points of an one dimensional dynamical system lyinginside the modulated phase. Such a phase, inherent in the Potts model has noanalogues in the Ising setting.

Phase diagram of the three states Potts model with next nearest neighbor interactions on the Bethe lattice