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arXiv:cond-mat/0312175 · Journal of Statistical Physics

Finite-Size Scaling in the Driven Lattice Gas

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

Published Mar 17, 2004• 26 citations
arXivHTMLPDF
DOI
10.1023/b:joss.0000019824.34397.1d

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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.
By identifying anisotropic scaling as the dominant feature of a lattice gas driven by a strong electric field, I obtain finite-size scaling forms by extending exact field-theoretic results. These are texted and supplemented by extensive Monte Carlo simulations in two dimensons. Excellent agreements are found. This resolves the disagreements between simulations and theories on the universality of the related models. Novel features of the finite-size effects of intrinsically anisotropic systems are emphasized.
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.