Kinetics of XY and Ising ordering in a time-dependent Ginzburg-Landau model with O(2)×Z_{2} ground-state degeneracy

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We investigate numerically the ordering dynamics of a time-dependent Ginzburg-Landau (TDGL) model in two dimensions, which possesses a ground-state manifold with $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ degeneracy. The ordering process of the system is described in terms of annihilation of both point defects (vortices) and line defects (domain walls), together with the mutual pinning between the two kinds of defects. There exist two regimes (regimes I and II) of parameter space with different growth kinetics. In regime I, Ising order shows a power law growth with exponent ${\ensuremath{\varphi}}_{I}\ensuremath{\simeq}0.48,$ but $\mathrm{XY}$ order grows with smaller exponent of ${\ensuremath{\varphi}}_{\mathrm{XY}}\ensuremath{\simeq}0.38,$ while in regime II both Ising and $\mathrm{XY}$ order exhibit an effective growth exponent of ${\ensuremath{\varphi}}_{I}\ensuremath{\sim}{\ensuremath{\varphi}}_{\mathrm{XY}}\ensuremath{\simeq}0.38.$ In regime II, the system exhibits a very slow approach to the asymptotic scaling regime. This distinction between the two regimes is attributed to the different nature of the symmetry of the Ising order parameter.