  We analyze recent experiments on the dilute rare-earth compound
LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a
Monte Carlo method we calculate the low-temperature behavior of the specific
heat and linear susceptibility, and compare our results to measurements. In our
model the susceptibility follows a Curie-Weiss law at high temperature, chi ~
1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x,
consistent with early experiments. We also find that the peak in the specific
heat scales linearly with dilution, C_max(T) ~ x, in disagreement with recent
experiments. Experimental studies do not reach a consensus on the functional
form of these quantities, and in particular we do not see reported scalings of
the form chi ~ T^-0.75 and chi ~ exp(-T/T_0). Furthermore we calculate the
ground state magnetization as a function of dilution, and re-examine the phase
diagram around the critical dilution x_c=0.24(3). We find that the spin glass
susceptibility for the Ising model does not diverge below x_c, while recent
experiments give strong evidence for a stable spin-glass phase in
LiHo_0.167Y_0.833F_4.
