Phase separation of the Potts model in the square lattice

When the two dimensional q-color Potts model in the square latticeis quenched at zero temperature with Glauber dynamics, the energy decreases intime following an Allen-Cahn power law, and the system converges to a phase withenergy higher than the ground state energy after an arbitrary large time whenq > 4. At low but finite temperature, it cesses to obey the power-law regime andorders after a very long time, which increases with q, and before which it performsa domain growth process which tends to be slower as q increases. We briefly presentand comment numerical results on the ordering at nonzero temperature.