  We study the effective long-range Ising dipole model with a local exchange
interaction appropriate for the dilute magnetic compound LiHo_{x}Y_{1-x}F_4.
Our calculations yield a value of 0.12 K for the nearest neighbor exchange
interaction. Using a Monte Carlo method we calculate the phase boundary T_c(x)
between the ferromagnetic and paramagnetic phases. We demonstrate that the
experimentally observed linear decrease in T_c with dilution is not the simple
mean-field result, but a combination of the effects of fluctuations, the
exchange interaction and the hyperfine coupling. Furthermore, we find a
critical dilution x_c=0.21(2), below which there is no ordering. In agreement
with recent Monte Carlo simulations on a similar model, we find no evidence of
the experimentally observed freezing of the glassy state in our calculation. We
apply the theory of Stephen and Aharony to LiHo_{x}Y_{1-x}F_4 and find that the
theory does predict a finite-temperature freezing of the spin glass. Reasons
for the discrepancies are discussed.
