Phase Diagram and Interfacial Instabilities in the Driven Widom-Rowlinson Lattice Gas

The Widom-Rowlinson lattice gas is a two-species model exhibiting phase
separation above a critical density and, under a drive, remarkable
properties such as lamellar ordering perpendicular to the drive, and kink
singularities in the structure factor [1]. Initial studies of the high-density
ordered phase were complicated by artifacts of the initial configuration.
These are now eliminated using a new method in which particles are slowly
added to the evolving system, allowing a pattern of the preferred wavelength
to emerge spontaneously. This method enables detailed study of the sequence
of transitions between stripe numbers with increasing system size at fixed
drive and density, and precise mapping of the boundary between disordered
and ordered phases as reflected in the order parameter and the density of
interfacial sites. We also analyze the instability of an interface oriented
along the drive, characterized by an exponential-growth regime in the amplitude
of interface undulations and systematic increase of the dominant wavelength.
These undulations eventually connect via the periodic boundaries, yielding stripes
oriented perpendicular to the drive.

1. R. Dickman and R.K.P. Zia, Phys Rev. E 97, 062126 (2018).