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

By performing extensive Monte Carlo simulations we show that the infinitely fast driven lattice gas (IDLG) shares its critical properties with the randomly driven lattice gas (RDLG). All the measured exponents, scaling functions, and amplitudes are the same in both cases. This strongly supports the idea that the main relevant nonequilibrium effect in driven lattice gases is the anisotropy (present in both IDLG and RDLG) and not the particle current (present only in the IDLG). This result, at odds with the predictions from the standard theory for the IDLG, supports a recently proposed alternative theory. The case of finite driving fields is also briefly discussed.