Exact renormalization-group results for domain-growth scaling in spinodal decomposition.

Abstract

Scaling in late-stage spinodal decomposition is discussed using standard renormalization-group techniques. The equal-time correlation function has the scaling form C(r,t)=f(r/${t}^{1/z}$), with z=d+2-y, where z and (-y) are, respectively, the dynamical exponent and thermal eigenvalue for the zero-temperature fixed point and d is the spatial dimensionality. For a scalar order parameter, y=d-1 gives z=3, implying a domain growth law L(t)\ensuremath{\sim}${t}^{1/3}$. For a vector order parameter, y=d-2 gives z=4 and L(t)\ensuremath{\sim}${t}^{1/4}$.