Coarsening kinetics of a two-dimensional O(2) Ginzburg-Landau model: the effect of reversible mode coupling

We investigate, via numerical simulations, the phase ordering kinetics of a two-dimensional soft spin O(2) Ginzburg-Landau model when a reversible mode coupling is included via the conserved conjugate momentum of the spin order parameter (Model E). Coarsening of the system, when quenched from a disordered state to zero temperature, is observed to be enhanced by the existence of the mode coupling terms. The growth of the characteristic length scale L(t) exhibits an effective superdiffusive growth exponent that can be interpreted as a positive logarithmic-like correction to a diffusive growth, i.e., L(t) similar to (t ln t)(1/2). In order to understand this behavior, we introduced a simple phenomenological model of coarsening based on the annihilation dynamics of a vortex-antivortex pair, incorporating the effect of vortex inertia and logarithmically divergent mobility of the vortex. With a suitable choice of the parameters, numerical solutions of the simple model can fit the full simulation results very adequately. The effective growth exponent in the early time stage is larger due to the effect of the vortex inertia, which crosses over into the late time stage characterized by positive logarithmic correction to a diffusive growth. We also investigated the nonequilibrium autocorrelation function from which the so-called lambda exponent can be extracted. We get lambda similar or equal to 1.99(2) which is distinctly larger than the value of lambda similar or equal to 1.17 for the purely dissipative Model A dynamics of non-conserved O(2) models.