  The physics of the spin glass (SG) state, with magnetic moments (spins)
frozen in random orientations, is one of the most intriguing problems in
condensed matter physics. While most theoretical studies have focused on the
Edwards-Anderson model of Ising spins with only discrete `up/down' directions,
such Ising systems are experimentally rare. LiHo$_{x}$Y$_{1-x}$F$_{4}$, where
the Ho$^{3+}$ moments are well described by Ising spins, is an almost ideal
Ising SG material. In LiHo$_{x}$Y$_{1-x}$F$_{4}$, the Ho$^{3+}$ moments
interact predominantly via the inherently frustrated magnetostatic
dipole-dipole interactions. The random frustration causing the SG behavior
originates from the random substitution of dipole-coupled Ho$^{3+}$ by
non-magnetic Y$^{3+}$. In this paper, we provide compelling evidence from
extensive computer simulations that a SG transition at nonzero temperature
occurs in a realistic microscopic model of LiHo$_{x}$Y$_{1-x}$F$_{4}$, hence
resolving the long-standing, and still ongoing, controversy about the existence
of a SG transition in disordered dipolar Ising systems.
