Ordering kinetics in systems with long-range interactions.

Abstract

The growth kinetics following a quench from high temperatures to zero temperature is studied using the time-dependent Ginzburg-Landau model. We investigate d-dimensional systems with n-component order parameter and assume that the interactions decay with distance r as V^(r)\ensuremath{\sim}${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{d}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ with 02. The spherical limit (n=\ensuremath{\infty}) is solved for both conserved and nonconserved order-parameter dynamics and the scaling properties of the structure factor are calculated. We find scaling features (including multiscaling in the conserved case) that are similar to those of systems with short-range interactions. The essential difference is that the short-range value of the dynamic critical exponent ${\mathit{z}}_{\mathit{s}}$ is replaced by z=${\mathit{z}}_{\mathit{s}}$-2+\ensuremath{\sigma} and the form of the scaling function is modified. We also study the general n case for nonconserved order-parameter dynamics and calculate the structure factor in an approximate scheme with the results that (i) the spherical-limit value of z remains unchanged as n is decreased down to n=1 and (ii) the spatial correlations decay at large distances as ${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{d}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$.