  We use quantum Monte Carlo simulations to study the effect of disorder, in
the form of a disordered chemical potential, on the phase diagram of the hard
core bosonic Hubbard model in two dimensions. We find numerical evidence that
in two dimensions, no matter how weak the disorder, it will always destroy the
long range density wave order (checkerboard solid) present at half filling and
strong nearest neighbor repulsion and replace it with a bose glass phase. We
study the properties of this glassy phase including the superfluid density,
energy gaps and the full Green's function. We also study the possibility of
other localized phases at weak nearest neighbor repulsion, i.e. Anderson
localization. We find that such a phase does not truly exist: The disorder must
exceed a threshold before the bosons (at weak nn repulsion) are localized. The
phase diagram for hard core bosons with disorder cannot be obtained easily from
the soft core phase diagram discussed in the literature.
