Anisotropic Domain Structure in Late-Stage Coarsening

We study the asymptotic late stage of phase separation dynamics, where the characteristic domain size grows as a power of time, and the growth exponent and scaled domain structure are universal, behavior suggestive of a dynamical renormalization group (RG) fixed point. We consider in particular the influence of surface tension anistropy on the resulting growth and structure. Since this RG fixed point is not accessible via a controlled perturbation theory, we resort to simulations of the two-dimensional Cahn-Hilliard equation, modified to include an anisotropic surface tension. We find that anisotropy persists in the asymptotic state, modifying the domain structure but not the growth exponent. The Porod tail of the angle-resolved structure factor S(k,t) provides a sensitive diagnostic, which allows us to quantify the degree of anistropy in the scaled domain structure. Evidently the underlying RG fixed point must depend on the full shape of the surface tension anisotropy.