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

Abstract

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 A 0 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 L x , 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 ∝ λ p , where p depends on the temperature and L x . At low T ’s ( T ≪ T c ( E ) ) and large L x , p approaches to p = 3 / 2 . At intermediate T ’s ( T < T c ( E ) ), p decreases up to p ≈ 1 , and is free of finite effects. This indicates that the interface stabilizes faster than in the equilibrium model, i. e. the Ising lattice gas ( E = 0 ) where p = 3 . At higher T ’s p increases for T ≲ T c ( E ) , and the finite size dependence is recovered. Also, if T is fixed, p increases with L x until it saturates at large values of it, while this regime is vanishing at T ≲ T c ( E ) . In this way, the dynamic relaxation process of a sinusoidal interface is improved by the external driving field with respect to its equilibrium counterpart, if the system is set in an intermediate temperature stage far from T c ( E ) and in a lattice with a sufficiently large longitudinal side. The behavior of τ was also investigated as a function of E and in the intermediate stage T < T c ( E ) . It was found that τ decreases exponentially with E in the interval 0 < E ≲ 1 , while for higher fields it remains constant. The exponential decay depends on the wavelength of the initial profile. In order to study the spatial evolution of the profiles, we evaluated the structure factor of the interface, and the Fourier coefficients corresponding to the same wave vector of the initial profile. The obtained results allowed us to conclude that the spatial evolution of the profile maintains its initial wavelength, does not travel along the external field axis, and its shape is preserved over all the relaxation process.