Phase separation and random domain patterns in a stochastic particle model

This paper deals with a dynamics (Glauber-Kawasaki) of a d-dimensional (d = 2,3) spin system, with a (zero magnetization) Bernoulli measure as initial condition. On the hydrodynamic scaling the system is reacting and diffusive, and the associated macroscopic initial state is stationary, but unstable. We prove that the system will escape from this spatially trivial state on a time scale longer than the hydrodynamic one (on this new scale the escape will happen at a deterministic time). Right after the escape the system will have locally a magnetization corresponding to one of the two stable phases, but globally it will show a nontrivial spatial structure. The onset of this spatial structure is studied and its characterization by means of a random field is given. This work extends the results in De Masi (1991) that deal with a one-dimensional system.