Is the particle current a relevant feature in driven lattice gases?

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.

Short-Time Behavior and Criticality of Driven Lattice Gases

The nonequilibrium short-time critical behaviors of driven and undriven lattice gases are investigated via Monte Carlo simulations in two spatial dimensions starting from a fully disordered initial configuration. In particular, we study the time evolution of suitably defined order parameters, which account for the strong anisotropy introduced by the homogeneous drive. We demonstrate that, at short times, the dynamics of all these models is unexpectedly described by an effective continuum theory in which transverse fluctuations, i.e., fluctuations averaged along the drive, are Gaussian, irrespective of this being actually the case in the stationary state. Strong numerical evidence is provided, in remarkable agreement with that theory, both for the driven and undriven lattice gases, which therefore turn out to display the same short-time dynamics.

Far-from-equilibrium growth of magnetic thin films with Blume-Capel impurities

We investigate the irreversible growth of (2+1)-dimensional magnetic thin films. The spin variable can adopt three states (s(I)=±1,0), and the system is in contact with a thermal bath of temperature T. The deposition process depends on the change of the configuration energy, which, by analogy to the Blume-Capel Hamiltonian in equilibrium systems, depends on Ising-like couplings between neighboring spins (J) and has a crystal field (D) term that controls the density of nonmagnetic impurities (s(I)=0). Once deposited, particles are not allowed to flip, diffuse, or detach. By means of extensive Monte Carlo simulations, we obtain the phase diagram in the crystal field vs temperature parameter space. We show clear evidence of the existence of a tricritical point located at D(t)/J=1.145(10) and k(B)T(t)/J=0.425(10), which separates a first-order transition curve at lower temperatures from a critical second-order transition curve at higher temperatures, in analogy with the previously studied equilibrium Blume-Capel model. Furthermore, we show that, along the second-order transition curve, the critical behavior of the irreversible growth model can be described by means of the critical exponents of the two-dimensional Ising model under equilibrium conditions. Therefore, our findings provide a link between well-known theoretical equilibrium models and nonequilibrium growth processes that are of great interest for many experimental applications, as well as a paradigmatic topic of study in current statistical physics.

Nonequilibrium relaxation and critical aging for driven Ising lattice gases

We employ Monte Carlo simulations to study the nonequilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density autocorrelation function in the nonequilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time autocorrelations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.

Approximate thermodynamic structure for driven lattice gases in contact

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. For both attractive and repulsive nearest-neighbor interactions among particles and for a wide range of parameter values, we find that, to a good approximation, one could define an intensive thermodynamic variable, such as the equilibrium chemical potential, that determines the final steady state for two initially separated driven lattice gases brought into contact. However, due to nontrivial contact dynamics, there are also observable deviations from this simple thermodynamic law. To illustrate the role of the contact dynamics, we study a variant of the zero-range process and discuss how the deviations could be explained by a modified large-deviation principle. We identify an additional contribution to the large-deviation function, which we call the excess chemical potential, for the variant of the zero-range process as well as the driven lattice gases. The excess chemical potential depends on the specifics of the contact dynamics and is in general a priori unknown. A contact dependence implies that, even though an intensive variable may equalize, the zeroth law could still be violated.

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.

Critical behavior of the two-dimensional randomly driven lattice gas

We investigate the critical behavior of the two-dimensional randomly driven lattice gas, in which particles are driven along one of the lattice axes by an infinite external field with randomly changing sign. A finite-size scaling (FSS) analysis provides novel evidences that this model is not in the same universality class as the driven lattice gas with a constant drive (DLG), contrarily to what has been recently reported in the literature. Indeed, the FSS functions of transverse observables (i.e., related to order-parameter fluctuations with wave vector perpendicular to the direction of the field) differ from the mean-field behavior--both predicted and observed in the DLG. In sharp contrast to the case of the DLG, FSS can be established only for rectangular lattices where the dimension in the direction of the field grows as the second power of the other dimension. Further, the transverse Binder cumulant does not vanish at the critical point.

Lennard-Jones and lattice models of driven fluids

We introduce a nonequilibrium off-lattice model for anisotropic phenomena in fluids. This is a Lennard-Jones generalization of the driven lattice-gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system--which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.

Dynamic behavior of anisotropic nonequilibrium driving lattice gases

It is shown that intrinsically anisotropic nonequilibrium systems relaxing by a dynamic process exhibit universal critical behavior during their evolution toward nonequilibrium stationary states. An anisotropic scaling ansatz for the dynamics is proposed and tested numerically. Relevant critical exponents can be evaluated self-consistently using both the short- and long-time dynamics frameworks. The obtained results allow us to clarify a long-standing controversy about the theoretical description, the universality, and the origin of the anisotropy of driven diffusive systems, showing that the standard field theory does not hold and supporting a recently proposed alternative theory.