Dynamic and spatial behavior of a corrugated interface in the driven lattice gas model

The spatiotemporal behavior of an initially corrugated interface in the two-dimensional driven lattice gas (DLG) model with attractive nearest-neighbors interactions is investigated via Monte Carlo simulations. By setting the system in the ordered phase, with periodic boundary conditions along the external field axis. i.e. horizontal, and open along the vertical directions respectively, an initial interface was imposed, that consists in a series of sinusoidal profiles with amplitude A0 and wavelength λ set parallel to the applied driving field axis. We studied the dynamic behavior of its statistical width or roughness W(t), defined as the root mean square of the interface position. We found that W(t) decays exponentially for all λ and lattice longitudinal sizes Lx, i.e., the lattice side that runs along the axis of the external field. We determined its relaxation time τ, and found that depends on λ as a power law τ∝λp, where p depends on the temperature and Lx. At low T’s (T Tc(E)) and large Lx, p approaches to p=3/2. At intermediate T’s (T