Potts model with next-nearest-neighbor ternary interactions on an arbitrary-order Cayley tree

Abstract

We study the phase diagrams for the Potts model with restricted competing nearest-neighbor interactions J 1 and ternary interactions J pt on a Cayley tree of arbitrary order k. At vanishing temperature, the phase diagram is fully determined for all values and signs of J pt /J 1 and T/J 1. The phase diagrams are obtained from stability conditions, and characteristic points in the iteration scheme are numerically analyzed. The wavevectors versus temperature are plotted for some critical points in the modulated phases. Then, we using the Lyapunov exponent to verify the stability of the periods.