A Potts model with infinitely degenerate ground state

A q-component Potts model with ferromagnetic and antiferromagnetic interactions in the two respective directions of a square lattice is considered. An argument is given showing that an order phase can exist in this model, even though the ground state is disordered and infinitely degenerate. The authors use the Migdal-Kadanoff transformation to obtain a closed-form expression for its critical point. They also carry out a Monte Carlo simulation of the model for q=3. The specific heat exhibits a broad maximum which does not sharpen appreciably as the lattice size is increased. This suggests that the phase transition if it exists, is of an unconventional type.