  Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of
much interest for over the past fifteen years. Their low temperature strongly
correlated state can be mapped onto the proton disordered state of common water
ice and, consequently, spin ices display the same low temperature residual
Pauling entropy as water ice. Interestingly, it was found in a previous study
[X. Ke {\it et. al.} Phys. Rev. Lett. {\bf 99}, 137203 (2007)] that, upon
dilution of the magnetic rare-earth ions (Dy^{3+} and Ho^{3+}) by non-magnetic
Yttrium (Y^{3+}) ions, the residual entropy depends {\it non-monotonically} on
the concentration of Y^{3+} ions. In the present work, we report results from
Monte Carlo simulations of site-diluted microscopic dipolar spin ice models
(DSIM) that account quantitatively for the experimental specific heat
measurements, and thus also for the residual entropy, as a function of
dilution, for both Dy2Ti2O7 and Ho2Ti2O7. The main features of the dilution
physics displayed by the magnetic specific heat data are quantitatively
captured by the diluted DSIM up to, and including, 85% of the magnetic ions
diluted (x=1.7). The previously reported departures in the residual entropy
between Dy2Ti2O7 versus Ho2Ti2O7, as well as with a site-dilution variant of
Pauling's approximation, are thus rationalized through the site-diluted DSIM.
For 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted, we find a
significant discrepancy between the experimental and Monte Carlo specific heat
results. We discuss some possible reasons for this disagreement.
