Equilibrium crystal shapes in the Potts model
arXiv:cond-mat/0011336 · doi:10.1103/PhysRevE.64.016125
Abstract
The three-dimensional -state Potts model, forced into coexistence by fixing the density of one state, is studied for , 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 . We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing , 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 scale at the melting point.
6 pages, 3 figures, submitted to PRE