Domain-growth kinetics in the two-dimensional three-state chiral clock model

The growth of ordered domains in the two-dimensional chiral clock model following a quench from the disordered state to a low-temperature nonequilibrium state is studied by Monte Carlo simulation. The time-dependence of the mean-linear domain size R(t), the excess energy, and the dynamical structure factor is obtained as a function of the asymmetry parameter Δ. In general, periodic boundary conditions are used, but free surfaces are also applied in some cases. The growth exhibits at zero temperature two qualitatively different regimes, depending on Δ. In the dry part of the phase diagram, 0≤Δ≤0.25, the growth is algebraic, R(t)∼$t^n$, whereas it is pinned by vortex configurations in the wet part, Δ>0.25. The vortices cannot be annealed away with the employed updating algorthm. The kinetic exponent n, calculated from R(t) data from a lattice with 240×240 spins varies from 0.35 for Δ=0 to 0.50 for Δ=0.25. n could not be extracted from R(t) data for a smaller lattice with 120×120 spins. In contrast, the growth calculated from the structure factor shows only small finite-size effects. Analysis of the structure factor data leads to an estimate for n consistent with 0.5 for 0≤Δ≤0.25. Quenches to finite temperatures, T≃1/2$T_c$(Δ), show that temperature excitations can remove the zero-temperature pinning effects and that n is consistent with 0.5 (Δ>0.25). n is temperature independent within statistical error for 0≤Δ≤0.25.