Renormalization-group approach to domain-growth scaling

Abstract

A nonperturbative renormalization-group approach is used to discuss domain growth in late-stage spinodal decomposition. The central ideas are that a scaling limit, described by a zero-temperature (strong-coupling) fixed point, exists and that the (model B) conservation law does not permit any renormalization of the transport coefficient from the elimination of short-length scales. These two features lead to a simple relation between the exponent n that describes the time dependence of the characteristic domain size, L(t)∼${\mathit{t}}^{\mathit{n}}$, and the scaling dimension y of the Hamiltonian at the T=0 fixed point: 1/n==z=d+2-y, where d is the spatial dimension and z is a kind of dynamical exponent associated with the T=0 fixed point. The Lifshitz-Slyosov result n=1/3 follows from y=d-1. Results for the temperature dependence of the growth law are obtained for both conserved and nonconserved dynamics. To exemplify the power of the method, the Lifshitz-Slyosov result is generalized to systems with (power-law) long-range diffusion. Crossover to the nonconserved results is predicted, implying that the conservation law becomes irrelevant, when the diffusion is sufficiently long ranged.