${\rm LiHo_xY_{1-x}F_4}$ in the highly-diluted limit

The rare-earth material ${\rm LiHo_xY_{1-x}F_4}$ has attracted much attention recently, not only because it is well described by a long-range dipolar Ising model, but also because it has a rich phase diagram in the temperature--concentration plane that makes it especially interesting to explore exotic magnetic phenomena. The existence of a spin-glass phase in this material has been a long-standing controversy. In particular, it is unclear if the spin-glass phase extends to the low-concentration limit, or if an exotic anti-glass state emerges. Using large-scale Monte Carlo simulations we probe this difficult regime of the phase diagram.