Two-time correlations, self-averaging, and an analytically solvable model of phase-ordering dynamics

We consider a simple model of phase-ordering dynamics with nonconserved order parameter introduced by Ohta, Jasnow, and Kawasaki. We demonstrate that, within this model, any expectation value, including multiple-time-correlation functions, can be obtained. Although the dynamics are very simple and are spatially non-self-averaging only in a trivial sense, much of the seemingly complex behavior seen in simulations of more realistic models is reproduced. The model of Ohta et al. also suggests a new type of dynamical universality class that is characterized by the lack of temporal, as opposed to spatial, self-averaging. The predictions of this model are found to agree well with numerical experiments.