Domain-growth kinetics for theQ-state Potts model in two and three dimensions

Abstract

We present new simulations of the domain-growth kinetics for the Q-state Potts model in two and three dimensions. The time dependence of the average grain radius R¯ can be described by R¯≃${\mathrm{Bt}}^n$, where B is a temperature-dependent constant. In two dimensions, we find n=0.49±0.02 for a range of Q values from 2 to 48. This value of n is obtained from very long simulations on lattices up to size ${1000}^2$ and is in contrast to our earlier estimates for n which were less than (1/2 (n≃0.41±0.01) for large Q. In three dimensions on lattices of size ${100}^3$, we find that n=0.48±0.04 if early-time data are excluded from the fit to the kinetic data but smaller if the entire data set is used. The grain-size distribution for several values of Q in both two and three dimensions is also determined and compared with our results for grain growth in real polycrystalline materials.