Journal of Statistical Physics, Vol. 66, Nos. 3/4, 1992. p. 1101-1122.
We study the applicability of parallelized/vectorized Monte Carlo (MC) algorithms to the simulation of domain growth in two-dimensional lattice gas models undergoing an ordering process after a rapid quench below an order-
disorder transition temperature. As examples we consider models with 2 x 1 and c(2x2) equilibrium superstructures on the square and rectangular lattices, respectively. We also study the case of phase separation ("1 x 1" islands) on the square lattice. A generalized parallel checkerboard algorithm for Kawasaki dynamics is shown to give rise to artificial spatial correlations in all three models. However, only if superstructure domains evolve do these correlations modify the kinetics by influencing the nucleation process and result in a reduced growth exponent compared to the value from the conventional heat bath algorithm with random single-site updates. In order to overcome these artificial modifications, two MC algorithms with a reduced degree of parallelism ("hybrid" and "mask" algorithms, respectively) are presented and applied. As the results indicate, these algorithms are suitable for the simulation of super-structure domain growth on parallel/vector computers.