Dynamic behavior of the interface of strip-like structures in driven diffusive systems

TL;DR

This study investigates the dynamic interface behavior in driven lattice gas models using Monte Carlo simulations, revealing critical scaling regimes and estimating critical exponents, suggesting universality between models.

Contribution

It provides the first detailed numerical analysis of interface dynamics and critical exponents in driven lattice gas models, linking interface behavior to bulk criticality and universality.

Findings

Interface width saturation depends on lattice size and exhibits two regimes.

Estimated anisotropic and dynamic critical exponents consistent with theoretical predictions.

Similar behavior observed in both standard and random driven lattice gas models.

Abstract

The 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 $W^{2}_{sat}\propto L_y^{2\alpha_I}$ near the critical zone, $\alpha_I=1/2$ 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 $\Delta_I\simeq 1$, in agreement with the computed value for anisotropic bulk exponent $\Delta_B$ 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 $W\propto t^{\beta_I}$, 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 $z_{\perp}^I\approx 4$, 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.