Kinetic models of ordering in two dimensions

The approach to equilibrium of ordered superlattice structures on surfaces is analyzed. Both Monte Carlo methods as well as analytic models of interacting domain-walls are used to study the kinetics of quenched, two dimensional systems with Q degenerate equilibrium states. In particular, the growth of long-range order in the magnetic analogs of the commensurate superlattice structures found on surfaces is analyzed in a study of the kinetics of typical domain geometric that are found, when systems are quenched from high (disordered state) to low temperatures. Calculations and simulations of the time and temperature dependence of the domain sizes for the model system of isolated domains indicate that for two dimensions roughening fluctuations of the domain-walls, strongly influence the grain growth kinetics. Strip-shaped domains approach equilibrium almost entirely through these fluctuations, while circular domains shrink due to deterministic curvature, but with a rate that is strongly temperature dependent even for temperatures outside the critical region.