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

Abstract

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 \ensuremath{\Delta}. 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 \ensuremath{\Delta}. In the dry part of the phase diagram, 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}0.25, the growth is algebraic, R(t)\ensuremath{\sim}${t}^{n}$, whereas it is pinned by vortex configurations in the wet part, \ensuremath{\Delta}>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\ifmmode\times\else\texttimes\fi{}240 spins varies from 0.35 for \ensuremath{\Delta}=0 to 0.50 for \ensuremath{\Delta}=0.25. n could not be extracted from R(t) data for a smaller lattice with 120\ifmmode\times\else\texttimes\fi{}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\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}0.25. Quenches to finite temperatures, T\ensuremath{\simeq}1/2${T}_{c}$(\ensuremath{\Delta}), show that temperature excitations can remove the zero-temperature pinning effects and that n is consistent with 0.5 (\ensuremath{\Delta}>0.25). n is temperature independent within statistical error for 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}0.25.