Absolute test for theories of phase-ordering dynamics

Numerical simulation results are presented for phase ordering in the O(n) model with nonconserved order parameter, for 1≤n≤d in dimensions d=2 and 3. The two-point correlation functions ${\mathit{C}}_{\mathrm{\phi }}$ and ${\mathit{C}}_{\mathrm{\phi }}^2$ of the order-parameter field and its square are obtained and compared with approximate analytic results obtained by treating the order-parameter field as a function of a Gaussian auxiliary field. Good agreement between theory and simulation is obtained when the functions ${\mathit{C}}_{\mathrm{\phi }}$ and ${\mathit{C}}_{\mathrm{\phi }}^2$ are considered separately, but not when the free parameter of the theory [incorporated in the scaling length L(t)] is eliminated by considering the two functions together.