Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We review recent progress in understanding the full phase diagram of a one-dimensional, driven, two-species lattice model [Lahiri and Ramaswamy, PRL 79 (1997) 1150] in which the mobility of each species depends on the density of the other. The model shows three phases. The first is characterised by phase separation of an exceptionally robust sort, termed Strong Phase Separation, which survives at all temperature. The second phase has trivial static correlations, but density fluctuations are transported by a pair of kinematic waves involving both species. In the most interesting case, the two linearised eigenmodes, although nonlinearly coupled, have different dynamic exponents. The third ``phase'' arises at the phase boundary between the first two. Here, the first species evolves autonomously, but its fluctuations influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, with density fluctuations persisting even in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law.