Phase diagram of the dilute magnet LiHoxY1-xF4

We study the effective long-range Ising dipole model with a local exchange interaction appropriate for the dilute magnetic compound LiHoxY1-xF4. 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 and the exchange interaction. 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 LiHoxY1-xF4 and find that the theory does predict a finite-temperature freezing of the spin glass. Reasons for the discrepancies are discussed.