Exact results for curvature-driven coarsening in two dimensions

Abstract

We consider the statistics of the areas enclosed by domain boundaries (‘‘hulls’’) during the curvaturedriven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh (A, t)=2c/(A+λt) , demonstrating the validity of dynamical scaling in this system, where c=1/8π 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/λt. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.