Driving driven lattice gases to identify their universality classes

Abstract

The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes to which they belong. 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 conditions. 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.

Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

“…Because ⟨𝑚⟩ is vanishingly small and differs from ⟨|𝑚|⟩, the phases fluctuations are pivotal. Indeed, FTS becomes almost perfect once lattices of different sizes hold an identical number of phases of size 𝑅 −1/𝑟 ; hence the spatial selfsimilarity [38] of the phases fluctuations is ensured by fixing 𝐿 −1 𝑅 −1/𝑟 , as shown in the inset in Fig. 5(a).…”

Phases fluctuations, self-similarity breaking and anomalous scalings in driven nonequilibrium critical phenomena

“…First, the revised FTS is generalized to the case of a weak externally applied field and sufficiently large lattice sizes to account for an intermediate revised FTS regime between the FSS and FTS regimes for small and large lattice sizes, respectively. Second, we specify the spatial and temporal self-similarities of the phases fluctuations in the theory by extending the picture of self-similarity [38] in space to real time. The Bressy exponents are then introduced to rectify the violated scalings when the selfsimilarity is broken.…”

“…As pointed out in the last sections, in order to fully describe the scaling behavior, it is essential to maintain an additional self-similarity, the extrinsic self-similarity. This additional self-similarity is to ensure that differentsized lattices are subject to different rates of driving in such a way that all systems contain identical number of either the fluctuating phases clusters [38] or their survival time intervals illustrated numerically in Fig. 1.…”

“…The renormalization-group theory of such driven nonequilibrium critical phenomena can be generalized to a weak external driving of an arbitrary form and a series of nonequilibrium phenomena, such as negative susceptibility and competition of various equilibrium and nonequilibrium regimes and their crossovers, as well as the violation of fluctuation-dissipation theorem and hysteresis, arise from the competition of the various timescales stemming from the parameters of the driving [5]. FTS has also been successfully applied to many systems both theoretically [5,25,[27][28][29][30][31][32][33][34][35][36][37][38][39] and experimentally [40,41]. Equilibrium and nonequilibrium initial conditions have also been considered [5,42].…”

Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point

“…The FTS theory has been verified in the driven critical dynamics of the Rydberg atomic systems [37]. Furthermore, these full scaling forms have been employed to numerically detect the critical properties in both classical and quantum phase transitions [43][44][45][46][47][48][49].…”