Perpendicular and Parallel Phase Separation in Two Species Driven Diffusive Lattice Gases

We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbour attractive/repulsive interaction between particles of the same/opposite species. We discuss the connections between these results and the behaviour found in off-lattice systems, including laning and freezing by heating.