Self-consistent solution of phase separation with competing interactions

We present a solution of a modified time-dependent Ginzburg-Landau equation in the limit of infinite order-parameter dimension N. The scalar (N=1) model is believed to describe phase separation in chemically reactive binary mixtures, block copolymers, and other systems where competing short-range and long-range interactions give rise to steady-state, spatially periodic structures. We present exact analytical expressions for the time dependence of the dynamic structure factor S(k,t) and the peak position ${\mathit{k}}_{\mathit{m}}$(t). We compare the scaling behavior for N=∞ with that observed in the scalar model.