Correlators in phase-ordering from Schrödinger-invariance

Abstract

Systems undergoing phase-ordering kinetics after a quench into the ordered phase with $0<T<T_c$ from a fully disordered initial state and with a non-conserved order-parameter have the dynamical exponent $z=2$. The long-time behaviour of their single-time and two-time correlators, determined by the noisy initial conditions, is derived from Schrödinger-invariance and we show that the generic ageing scaling forms of the correlators follow from the Schrödinger covariance of the four-point response functions. The autocorrelation exponent $\hat{I}»$ is related to the passage exponent $\hat{I}{\P }_p$ which describes the time-scale for the cross-over into the ageing regime. Both Porod's law and the bounds $d/2\le \hat{I}»\le d$ are reproduced in a simple way. The dynamical scaling in fully finite systems and of global correlators is found and the low-temperature generalisation $\hat{I}»=d-2\hat{I}˜$ of the Janssen-Schaub-Schmittmann scaling relation is derived.

Latex2e, 1+33 pages, 1 figure included, final version