Theory of spinodal decomposition in relaxational tricritical models

Abstract

We present a theory for the late-stage spinodal decomposition for two relaxational tricritical models in which the order parameter is nonconserved and the subsidiary order parameter is either conserved or nonconserved. We find that for $d$-dimensional systems (for $d>1$) the characteristic domain size grows in proportion to ${t}^{\frac{1}{3}}$ (Lifshitz-Slyozov) and ${t}^{\frac{1}{2}}$ (Cahn-Allen-Chan), respectively, where $t$ is the time. A discussion is also given for the growth mechanism of a one-dimensional model. Our analysis in general involves linearizing the dynamical equations of motion around a stationary, but unstable state, which describes coexisting phases.