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arXiv:cond-mat/0106221

Finite-Size Critical Behavior of the Driven Lattice Gas

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

Published Jun 12, 2001• 0 citations
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Abstract

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 $γ$ and $ν$. 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.

DOI
10.48550/arxiv.cond-mat/0106221

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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.
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.
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We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional O(3)O(3)O(3) and $O(\ensuremath{\infty})$ \ensuremath{\sigma} models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.
A new application of finite size scaling to Monte Carlo simulations is introduced. Using this technique, critical behavior can be investigated at temperatures arbitrarily close to the critical point without large lattice sizes. Applying this method to the two-dimensional standard O(3) model it is shown that for the correlation length asymptotic scaling holds for \ensuremath{\beta}\ensuremath{\ge}2.25; the magnetic susceptibility converges to the asymptotic scaling very slowly. In the scaling region, it is observed that the specific heat decreases with \ensuremath{\beta}, which implies no singular behavior of the specific heat for this model.
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