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arXiv:cond-mat/0507614 · Physical Review E

Critical behavior of the two-dimensional randomly driven lattice gas

Sergio Caracciolo A, Andrea Gambassi, Massimiliano Gubinelli, Andrea Pelissetto C

Published Nov 9, 2005• 11 citations
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Abstract

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.

DOI
10.1103/physreve.72.056111

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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.
We present a detailed Monte Carlo study of the high-temperature phase of the two-dimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, study its finite-size-scaling behavior and extrapolate it to the infinite-volume limit by using an iterative extrapolation method. The same method is applied to the susceptibility. We determine the transverse exponents γγγ and ννν. They turn out to be in perfect agreement with the theoretical predictions. We also compute the transverse Binder parameter, which apparently vanishes at the critical point, and the distribution of the magnetization. These results confirm the Gaussian nature of the transverse excitations.
The dynamic and static critical behaviors of driven and equilibrium lattice gas models are studied in two spatial dimensions. We show that in the short-time regime immediately following a critical quench, the dynamics of the transverse anisotropic order parameter, its autocorrelation, and Binder cumulant are consistent with the prediction of a Gaussian, i.e., noninteracting, effective theory, both for the nonequilibrium lattice gases and, to some extent, their equilibrium counterpart. Such a superuniversal behavior is observed only at short times after a critical quench, while the various models display their distinct behaviors in the stationary states, described by the corresponding, known universality classes.
It is shown by the Monte Carlo method that finite-size scaling (FSS) holds in the two-dimensional randomly coupled Ising ferromagnet. It is also demonstrated that the form of the universal FSS function constructed via a FSS scheme depends on the strength of the random coupling in the case of strongly disordered systems. Monte Carlo measurements of thermodynamic (infinite-volume-limit) data of the correlation length $(\ensuremath{\xi})$ up to $\ensuremath{\xi}\ensuremath{\simeq}200$ along with measurements of the fourth-order cumulant ratio (Binder cumulant ratio) at criticality are analyzed in light of two competing scenarios of weak universality and the multiplicative logarithmic correction. It is demonstrated that the data are likely to be more consistent with the former scenario than the latter which is the conventional scenario.
We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.
We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.
We define a transverse correlation length suitable to discuss the finite-size scaling behaviour of an out-of-equilibrium lattice gas, whose correlation functions decay algebraically with the distance. By numerical simulations we verify that this definition has a good infinite-volume limit independent of the lattice geometry. We study the transverse fluctuations as they can select the correct field-theoretical description. By means of a careful finite-size scaling analysis, without tunable parameters, we show that they are Gaussian, in agreement with the predictions of the field theory proposed by Janssen, Schmittmann, Leung and Cardy.