Domain growth and nucleation in a discrete bistable system

Abstract

A cubic map lattice, which consists of an array of cubic discrete-time maps coupled through nearest-neighbor diffusion interactions, is studied in a parameter region where the isolated maps possess bistable steady states. Within this parameter region, the spatio-temporal evolution of this deterministic dynamical system exhibits the phenomena of phase separation and nucleation. When the two coexisting states have the same stability, the domain growth is like that for continuous systems with a nonconserved order parameter, and follows Allen-Cahn scaling on long distance and time scales. When the states have different stabilities, growth typically occurs by a nucleation process. In addition to exploring these phenomena, which have their analogs in continuous systems, features of the inhomogeneous states peculiar to the discrete model are also investigated.