  We study the time correlation function of a density field in two-dimensional
driven diffusive systems within the framework of fluctuating hydrodynamics. It
is found that the time correlation exhibits power-law behavior in an
intermediate time regime in the case that the fluctuation-dissipation relation
is violated and that the power-law exponent depends on the extent of this
violation. We obtain this result by employing a renormalization group method to
treat a logarithmic divergence in time.
