Perturbation Expansion in Phase-Ordering Kinetics: II. N-vector Model

TL;DR

This paper extends the perturbation theory for phase-ordering kinetics to the n-vector model, providing explicit second-order corrections and analyzing their behavior in large dimensions and component limits.

Contribution

It generalizes the perturbation expansion to the n-vector model and computes second-order corrections for nonequilibrium exponents.

Findings

Second-order corrections are explicitly derived in d dimensions.

Corrections vanish in large n and d limits.

Large-d convergence of corrections is exponential.

Abstract

The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in the scalar case, one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). The second-order corrections for the nonequilibrium exponents are worked out explicitly in $d$ dimensions and as a function of the number of components $n$ of the order parameter. In the formulation developed here the corrections to the OJK results are found to go to zero in the large $n$ and $d$ limits. Indeed, the large-$d$ convergence is exponential.