Driving driven lattice gases to identify their universality classes

The critical behaviors of driven lattice gas models have been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in their universality classes. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their respective nonequilibrium critical points into further nonequilibrium situations. Employing the theory of finite-time scaling, we are able to unambiguously discriminate the universality classes between the two models. In particular, the infinitely driven lattice gas and the randomly driven lattice gas models belong to different universality classes. These results show that finite-time scaling is effective even in nonequilibrium phase transitions.

Figure 1

$M$ and $g$ and their scalings of the IDLG model using the exponents of SFT for (a)–(d), ${\mathcal{C}}_{\perp }=5.4$ and ${\mathcal{C}}_{\parallel }=4.92$, and (e)–(h), ${\mathcal{C}}_{\perp }=6$ and ${\mathcal{C}}_{\parallel }=2.16$. The dashed lines in (b) and (f) locate the critical temperature. The insets in (d) and (h) show the original $g$ curves. Each column of panels shares an identical abscissa and each row shares the same legend which lists $L_{\perp }\times L_{\parallel }$.

Figure 2

$M$ and $g$ and their scalings of the IDLG model using the exponents of AFT instead of SFT for ${\mathcal{C}}_{\perp }=5.70$ and ${\mathcal{C}}_{\parallel }=16.3$. The dashed line in (b) marks the cross point, which is applied to (c) and (d) for curve collapses. The inset in (d) shows the original $g$ curves. All panels share the same legend.

Figure 3

$M$ and $g$ and their scalings of the RDLG model using the exponents of AFT for ${\mathcal{C}}_{\perp }=5.70$ and ${\mathcal{C}}_{\parallel }=16.3$. The dashed line in (b) marks $T_c$. The inset in (d) shows the original $g$ curves. All panels share the same legend.