From ordered bubbles to random stripes: Pattern formation in a hydrodynamic lattice gas

A two-component momentum-conserving lattice gas with competing interactions is introduced in two dimensions. One interaction acts at short range and produces interfaces with surface tension. The second interaction, the negative of the first, acts at rangea and produces modulated structures with approximate wavelength 2a. Depending on particle density, species concentration, and relative interaction strength, the equilibrium patterns formed by the model range from isotropic mixed and unmixed phases to hexagonally-ordered bubbles to randomly-oriented stripes. A Ginzburg-Landau equation is proposed that qualitatively captures the basic features of these phase transitions.