Kinetics of ordering in two dimensions. II. Quenched systems

An efficient Monte Carlo procedure is applied to the study of the kinetics of low- and high-Q Potts models on surfaces quenched from a high temperature (TT₂) to low temperatures (T0. 5T₂, the exponent n decreases from 12 for Q=2 (Ising model) to approximately 0. 41 for large Q. The distribution of grain sizes and shapes is also calculated from the results of the simulations. For large Q, these distributions are time independent. On the square lattice at low temperatures the growth exponent is approximately equal to 0, due to the nucleation of pinned domains. The Monte Carlo results are discussed in terms of experimental studies of the ordering of adsorbed atoms on surfaces and of the growth of grains in polycrystalline materials.