  We explore the effects of various kinds of random disorder on the
quasiparticle density of states of two-dimensional d-wave superconductors using
an exact real-space method, incorporating realistic details known about the
cuprates. Random on-site energy and pointlike unitary impurity models are found
to give rise to a vanishing DOS at the Fermi energy for narrow distributions
and low concentrations, respectively, and lead to a finite, but suppressed, DOS
at unrealistically large levels of disorder. Smooth disorder arising from
impurities located away from the copper-oxide planes meanwhile gives rise to a
finite DOS at realistic impurity concentrations. For the case of smooth
disorder whose average potential is zero, a resonance is found at zero energy
for the quasiparticle DOS at large impurity concentrations. We discuss the
implications of these results on the computed low-temperature specific heat,
the behavior of which we find is strongly affected by the amount of disorder
present in the system. We also compute the localization length as a function of
disorder strength for various types of disorder and find that intermediate- and
high-energy states are quasi-extended for low disorder, and that states near
the Fermi energy are strongly localized and have a localization length that
exhibits an unusual dependence on the amount of disorder. We comment on the
origin of disorder in the cuprates and provide constraints on these based on
known results from scanning tunneling spectroscopy and specific heat
experiments.
