Kinetics of phase ordering on curved surfaces

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intrasurface kinetics of phase o rdering on corrugated surfaces. Geometrical dynamical equations are derived for the domain interfaces. The dynamics is shown to depend strongly on the local Gaussian curvature of the surface, and can be fundamentally differen t from that in flat systems: dynamical scaling breaks down despite the pers istence of the dominant interfacial undulation mode; growth laws are slower than t(1/2) and even logarithmic; a new very-late-stage regime appears cha racterized by extremely slow interface motion; finally, the zero-temperatur e fixed point no longer exists, leading to metastable states. Criteria for the existence of the latter are derived and discussed in the context of mor e complex systems.