Asymptotic structure factor and power-law tails for phase ordering in systems with continuous symmetry

Abstract

We compute the asymptotic structure factor ${\mathit{S}}_{\mathbf{k}}$(t) [=L(t${)}^{\mathit{d}}$g(kL(t)), where L(t) is a time-dependent characteristic length scale and d is the dimensionality] for a system with a nonconserved n-component vector order parameter quenched into the ordered phase. The well-known Ohta-Jasnow-Kawasaki-Yalabik-Gunton result is recovered for n=1. The scaling function g(x) has the large-x behavior g(x)\ensuremath{\sim}${\mathit{x}}^{\mathrm{\ensuremath{-}}(\mathit{d}+\mathit{n})}$, which includes Porod's law (for n=1) as a special case.