Microemulsions in the driven Widom-Rowlinson lattice gas*

The driven Widom-Rowlinson lattice gas exhibits a remarkable non-equilibrium steady state in which uniform stripes form perpendicular to the drive direction. We study this model at low particle densities in two- and three-dimensions, where we find a disordered phase with a characteristic length scale (similar to a “microemulsion”). We develop a continuum theory of this disordered phase and derive a coarse-grained field-theoretic action for the non-equilibrium dynamics, making predictions for the dynamic structure factors. The system may be described via two coupled fields, a "charge" and overall particle density field, which have structure factors with different characteristic velocities, generated by an interplay between the nearest neighbor exclusion rule and the drive. We then show how fluctuation corrections may generate the "microemulsion" phase and speculate on the origin of a characteristic linear cusp in the static structure factor. This work lays the foundation for understanding the stripe phenomenon more generally and points toward a new kind of non-equilibrium pattern-forming phase transition.