Phase-Ordering Dynamics with an Order-Parameter-Dependent Mobility: The Large-n Limit

TL;DR

This paper investigates the phase-ordering dynamics of systems with an order-parameter-dependent mobility in the large-n limit, revealing how the vanishing of mobility influences growth laws and multi-scaling behavior.

Contribution

It provides an exact solution for large-n systems with order-parameter-dependent mobility, analyzing both conserved and non-conserved cases and their scaling properties.

Findings

Correlation length grows as a power of time in non-conserved case.

Structure factor exhibits multi-scaling with two length scales in conserved case.

Growth rates depend on how mobility vanishes near equilibrium.

Abstract

The effect of an order-parameter dependent mobility (or kinetic coefficient), on the phase-ordering dynamics of a system described by an n-component vector order parameter is addressed at zero temperature in the large-n limit. We consider cases in which the mobility or kinetic coefficient vanishes when the magnitude of the order parameter takes its equilibrium value. In the large-n limit, the system is exactly soluble for both conserved and non-conserved order parameter. In the non-conserved case, the scaling form for the correlation function and it's Fourier transform, the structure factor, is established, with the characteristic length growing as a power of time. In the conserved case, the structure factor is evaluated and found to exhibit a multi-scaling behaviour, with two growing length scales differing by a logarithmic factor. In both cases, the rate of growth of the length scales depends on the manner in which the mobility or kinetic coefficient vanishes as the magnitude of the order parameter approaches its equilibrium value.