Equilibrium crystal shapes in the Potts model

R. P. Bikker; G. T. Barkema; H. van Beijeren

doi:10.1103/physreve.64.016125

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Equilibrium crystal shapes in the Potts model

R. P. Bikker·G. T. Barkema·H. van Beijeren

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Abstract

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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R. P. Bikker, G. T. Barkema, H. van Beijeren. 2000-11-20. Equilibrium crystal shapes in the Potts model. https://doi.org/10.1103/physreve.64.016125

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