The Energy-Scaling Approach to Phase-Ordering Growth Laws

TL;DR

This paper introduces a unified scaling approach to determine phase-ordering growth laws in various systems, linking defect types and energy decay to the evolution of characteristic length scales.

Contribution

It presents a self-consistent method based on pair correlation scaling to derive growth laws across different models and defect types.

Findings

Derived growth laws for conserved and non-conserved $O(n)$ models.

Linked defect types to specific growth behaviors and energy decay.

Established generalized Porod laws for systems with textures.

Abstract

We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines $L(t)$ self-consistently for purely dissipative dynamics by computing the time-dependence of the energy in two ways. We derive growth laws for conserved and non-conserved $O(n)$ models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid-crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.