Dynamic behavior of the interface of striplike structures in driven lattice gases

In this work, the dynamic behavior of the interfaces in both the standard and random driven lattice gas models (DLG and RDLG, respectively) is investigated via numerical Monte Carlo simulations in two dimensions. These models consider a lattice gas of density rho=12 with nearest-neighbor attractive interactions between particles under the influence of an external driven field applied along one fixed direction in the case of the DLG model, and a randomly varying direction in the case of the RDLG model. The systems are also in contact with a reservoir at temperature T . Those systems undergo a second-order nonequilibrium phase transition between an ordered state characterized by high-density strips crossing the sample along the driving field, and a quasilattice gas disordered state. For T less, similarT_{c} , the average interface width of the strips (W) was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value W_{sat};{2} only depends on the lattice size parallel to the external field axis L_{y} and exhibits two distinct regimes: W_{sat};{2} proportional, variantlnL_{y} for low temperatures, that crosses over to W_{sat};{2} proportional, variantL_{y};{2alpha_{I}} near the critical zone, alpha_{I}=12 being the roughness exponent of the interface. By using the relationship alpha_{I}=1(1+Delta_{I}) , the anisotropic exponent for the interface of the DLG model was estimated, giving Delta_{I} approximately 1 , in agreement with the computed value for anisotropic bulk exponent Delta_{B} in a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of W at T_{c} was also monitored and shows two growing stages: first one observes that W proportional, variantlnt for several decades, and in the following times one has W proportional, variantt;{beta_{I}} , where beta_{I} is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving z_{ perpendicular};{I} approximately 4 , which is consistent with the dynamic exponent of the bulk critical transition z_{ perpendicular};{B} in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.