Phase separation and growth in a two-variable discrete model

Phase separation and domain growth are studied in a two-variable discrete-space and discrete-time model of a species competition process. The system is characterized by two order parameters. When the two competing states have equal stabilities, the domain evolution is similar to that in other physical systems with a nonconserved order parameter. The discrete model exhibits Allen-Cahn scaling for long times. When the two states have different stabilities, domain growth occurs by a nucleation mechanism. The existence of two order parameters introduces interesting features in the analysis of the boundary layer structure.