Perturbation Expansion in Phase-Ordering Kinetics: I. Scalar Order Parameter

TL;DR

This paper develops a perturbation theory for phase-ordering kinetics with a scalar order parameter, extending the Ohta-Jasnow-Kawasaki theory by calculating corrections and introducing a new decay exponent.

Contribution

It introduces a systematic perturbation expansion for phase-ordering kinetics, providing corrections to existing models and defining a new decay exponent for the order parameter.

Findings

Corrections to the OJK nonequilibrium exponent λ

Introduction of a new exponent ν for decay behavior

Extension of the theory to d-dimensional systems

Abstract

A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At the next nontrivial order in the expansion, worked out in d dimensions, one has small corrections to the OJK result for the nonequilibrium exponent $\lambda$ and the introduction of a new exponent $\nu$ governing the algebraic component of the decay of the order parameter scaling function at large scaled distances.