Equilibrium crystal shapes in the Potts model

Details Equilibrium crystal shapes in the Potts model Equilibrium crystal shapes in the Potts model

2000-11-20

arxiv.org/abs/cond-mat/0011336v1

Physics

Condensed Matter

6 pages, 3 figures, submitted to PRE

Scientific paper

10.1103/PhysRevE.64.016125

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 scale at the melting point.

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