Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling

TL;DR

This study uses numerical simulations to analyze how reversible mode coupling influences phase ordering kinetics in a 2D O(2) Ginzburg-Landau model, revealing enhanced coarsening and a super-diffusive growth behavior.

Contribution

It introduces a phenomenological model incorporating vortex inertia and mobility effects, explaining the super-diffusive growth and autocorrelation behavior observed.

Findings

Coarsening is enhanced by reversible mode coupling.

Growth law exhibits a (t ln t)^{1/2} behavior.

Autocorrelation exponent λ ≈ 2, larger than purely dissipative models.

Abstract

We investigate, via numerical simulations, the phase ordering kinetics of a two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode cou- pling is included via the conserved conjugate momentum of the spin order parameter (the model E). Coarsening of the system, when quenched from a dis- ordered 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 super-diffusive growth exponent that can be interpreted as a positive logarithmic-like correction to a diffusive growth, i.e., L(t) ~ (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 late time stage characterized by positive logarithmic correction to a diffusive growth. We also investigated the non-equilibrium autocorrelation function from which the so called {\lambda} exponent can be extracted. We get {\lambda} = 1.99(2) which is distinctively larger than the value of {\lambda} = 1.17 for the purely dissipative model-A dynamics of non-conserved O(2) models.