Microemulsions in the driven Widom-Rowlinson lattice gas

TL;DR

This paper explores the microemulsion phase in a driven two- and three-dimensional Widom-Rowlinson lattice gas, developing a continuum theory to explain the formation of characteristic length scales and stripe patterns under non-equilibrium conditions.

Contribution

It introduces a continuum field-theoretic model for the microemulsion phase in driven lattice gases, linking fluctuation corrections to observed structural features.

Findings

Identification of a microemulsion phase with a characteristic length scale

Development of a coupled driven diffusive systems field theory

Prediction of a peak in the static structure factor

Abstract

An investigation of the two-dimensional Widom-Rowlinson lattice gas under an applied drive uncovered a remarkable non-equilibrium steady state in which uniform stripes (reminiscent of an equilibrium lamellar phase) form perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E 97, 062126 (2018)]. Here we study this model at low particle densities in two and three dimensions, where we find a disordered phase with a characteristic length scale (a "microemulsion") along the drive direction. We develop a continuum theory of this disordered phase to derive a coarse-grained field-theoretic action for the non-equilibrium dynamics. The action has the form of two coupled driven diffusive systems with different characteristic velocities, generated by an interplay between the particle repulsion and the drive. We then show how fluctuation corrections in the field theory may generate the characteristic features of the microemulsion phase, including a peak in the static structure factor corresponding to the characteristic length scale. This work lays the foundation for understanding the stripe phenomenon more generally.