  The spreading of density fluctuations in two-dimensional driven diffusive
systems is marginally anomalous. Mode coupling theory predicts that the
diffusivity in the direction of the drive diverges with time as $(\ln t)^{2/3}$
with a prefactor depending on the macroscopic current-density relation and the
diffusion tensor of the fluctuating hydrodynamic field equation. Here we
present the first numerical verification of this behavior for a particular
version of the two-dimensional asymmetric exclusion process. Particles jump
strictly asymmetrically along one of the lattice directions and symmetrically
along the other, and an anisotropy parameter $p$ governs the ratio between the
two rates. Using a novel massively parallel coupling algorithm that strongly
reduces the fluctuations in the numerical estimate of the two-point correlation
function, we are able to accurately determine the exponent of the logarithmic
correction. In addition, the variation of the prefactor with $p$ provides a
stringent test of mode coupling theory.
