Growth kinetics of systems with continuous symmetry

The phase-ordering dynamics of a time-dependent Ginzburg-Landau model for a nonconserved order parameter with O(n) symmetry is investigated. We demonstrate that the two-point order-parameter correlation function obeys scaling in the long-time limit. A closed-form equation of motion is derived for the asymptotic scaling function for general n and spatial dimensionality d. Our approach emphasizes the role of topological defects in governing the scaling regime of the ordering process. These defects are also responsible for the singular behavior of the equal-time correlation function at short distances, which leads to a modified Porod's law for the scattering form factor in Fourier space. We also treat the two-time correlation function and determine the nonequilibrium exponent that controls the power-law decay of the order-parameter autocorrelation function.