Possibilities and limitations of Gaussian-closure approximations for phase-ordering dynamics

The nonlinear equations describing phase-ordering dynamics can be closed by assuming the existence of an underlying Gaussian stochastic field which is nonlinearly related to the observable order-parameter field. We discuss the relation between different implementations of the Gaussian assumption and consider the limitations of this assumption for phase-ordering dynamics. The fact that the different approaches give different results is a sign of the breakdown of the Gaussian assumption. We discuss both the nonconserved and conserved order-parameter cases. We demonstrate that the Gaussian assumption cannot describe the large length-scale behavior in the latter case.