Phase separation in one-dimensional stochastic particle systems?

A class of interacting particle systems modelling driven diffusive systems with short range interactions has been suggested to exhibit macroscopic phase separation in d = 1 dimensions. Unlike all previously studied models exhibiting similar phenomena, there the phase separated state is fluctuating in the bulk of the macroscopic domains. We discuss a recently introduced sufficient criterion for the existence of such phase separation and point out some assumptions which require rigorous proof. We also introduce a new model for strong phase separation into essentially nonfluctuation states. We informally describe its exact invariant measure.