Equilibrium crystal shapes in the Potts model

The three-dimensional q-state Potts model, forced into coexistence by fixing the density of one state, is studied for q=2, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of q. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing q, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length settle at the melting point.