2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172281The dynamic behavior of the interfaces in the standard and random driven lattice gas models (DLG and RDLG respectively) is investigated via numerical Monte Carlo simulations in two dimensions. For $T\lesssim T_c$, 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 $W^{2}_{sat}$ only depends on the lattice size parallel to the external field axis $L_y$ and exhibits two distinct regimes: $W^{2}_{sat}\propto \ln$ $L_y$ for low temperatures, that crosses over to $W^{2}_{sat}\propto L_y^{2α_I}$ near the critical zone, $α_I=1/2$ being the roughness exponent of the interface. By using the relationship $α_I=1/(1+Δ_I)$, the anisotropic exponent for the interface of the DLG model was estimated, giving $Δ_I\simeq 1$, in agreement with the computed value for anisotropic bulk exponent $Δ_B$ with 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 $W \propto \ln$ $t$ for several decades, and in the following times one has $W\propto t^{β_I}$, where $β_{I}$ 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 $z_{\perp}^I\approx 4$, which is consistent with the dynamic exponent of the bulk critical transition $z_{\perp}^B$ 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.12 pages, 17 figuresStatistical Mechanicstext