A Variational Study of the Phase-diagram of the Potts 3 State Model Versus Monte-carlo Simulation

We study the phase diagram of the three-dimensional Z(3) spin model with nearest neighbour and next nearest ncighbour couplings by means of a variational method and compare its predictions with the results obtained with a Monte Carlo simulation. In this model, which is believed to belong to the same universality class as QCD at finite temperature, we found that a second order transition can occur at special values of the coupling