Phase-ordering dynamics of the O(<i>n</i>) model: Exact predictions and numerical results

Abstract

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the O(n) model with a nonconserved order parameter in spatial dimension 2\ensuremath{\le}d\ensuremath{\le}3 and spin dimension 1\ensuremath{\le}n\ensuremath{\le}d. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the d=2 O(2) model.