Perturbation Expansion in Phase Ordering Kinetics

TL;DR

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

Contribution

It introduces a systematic perturbation expansion that refines existing models and predicts new exponents in phase ordering dynamics.

Findings

Corrections to the nonequilibrium exponent λ are derived.

A new exponent ν governing decay at large distances is introduced.

Explicit calculations are provided in arbitrary dimensions.

Abstract

A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At next order, worked out explicitly 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.