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

TL;DR

This paper presents an exact phase diagram for the three-state Potts model with next nearest neighbor interactions on the Bethe lattice, revealing five phases including a novel paramodulated phase at low temperatures.

Contribution

It provides the first exact phase diagram for this model, identifying a new paramodulated phase unique to the Potts model on the Bethe lattice.

Findings

Identified five distinct phases including ferromagnetic, paramagnetic, modulated, antiphase, and paramodulated.

Discovered the paramodulated phase characterized by 2-periodic points inside the modulated phase.

All phases meet at the Lifshitz point at p=1/3.

Abstract

We have found an exact phase diagram of the Potts model with next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the Lifshitz point i.e. $p=1/3$. We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by 2-periodic points of an one dimensional dynamical system lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.