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

Abstract

We investigate, via numerical simulations, the phase ordering kinetics of a two-dimensional soft spinO(2) Ginzburg–Landau model when a reversible mode coupling is included via the conservedconjugate 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 bythe existence of the mode coupling terms. The growth of the characteristic length scaleL(t) exhibits an effective superdiffusive growth exponent that can be interpretedas a positive logarithmic-like correction to a diffusive growth, i.e.,L(t) ∼ (tlnt)1/2. In order to understand this behavior, we introduced a simple phenomenological model ofcoarsening based on the annihilation dynamics of a vortex–antivortex pair, incorporatingthe effect of vortex inertia and logarithmically divergent mobility of the vortex. With asuitable choice of the parameters, numerical solutions of the simple model can fit the fullsimulation results very adequately. The effective growth exponent in the early time stage islarger due to the effect of the vortex inertia, which crosses over into the late time stagecharacterized by positive logarithmic correction to a diffusive growth. We alsoinvestigated the nonequilibrium autocorrelation function from which the so-calledλ exponent can be extracted. We get which is distinctly larger than the value of for the purely dissipative Model A dynamics of non-conservedO(2) models.