Ordering kinetics of defect structures

TL;DR

This paper derives the order-parameter correlation function during phase-ordering kinetics in the O(n) model near defect cores, using conservation laws and a Gaussian approximation, resulting in the Ohta-Jasnow-Kawasaki form.

Contribution

It introduces a method to determine the correlation function using conservation equations and Gaussian assumptions in defect-dominated regimes.

Findings

Derived the correlation function in defect regimes

Connected conservation laws to known correlation forms

Validated the Ohta-Jasnow-Kawasaki solution

Abstract

We show how the continuity equations expressing conservation of topological point or string defect charge can be used to determine the order-parameter correlation function for the phase-ordering kinetics of the O(n) model in the special case where the order parameter is constrained to be near a defect core. In this regime we find a self-consistent solution by assuming the order parameter is Gaussian. The resulting linear equation for the order-parameter correlation function has as its solution the Ohta-Jasnow-Kawasaki form.