Biased diffusion of two species

A stochastic lattice gas with equal numbers of oppositely “charged” particles, diffusing under the influence of a uniform external “electric” field and the excluded volume condition, exhibits an order-disorder phase transition, controlled by particle density and field strength. Ordered configurations are spatially inhomogeneous, allowing for both zero and nontrivial winding numbers around toroidal lattices with periodic boundary conditions. We explore the transition and the structure of the ordered state, using both simulational and analytic tools.