Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model

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Abstract
Two-dimensional, infinitely degenerate Potts-model simulations were performed on four different lattices at zero and finite temperatures in order to examine the effects of lattice anisotropy and temperature on domain growth. The discrete lattice of the Potts model causes deviations from universal domain growth behavior by weakening the vertex angle boundary conditions that form the basis of von Neumann’s law. Smoothing the Wulff plot of the lattice (e.g., by extending spin interactions to a longer range) or increasing the temperature at which the simulation is performed can overcome the anisotropy inherent in discrete lattice simulations. Excellent overall agreement (kinetics, topological distribution, domain size distributions) between the low lattice anisotropy Potts-model simulations and the soap froth suggests that the Potts model is useful for studying domain growth in a wide variety of physical systems.