Spin Glass Transition at Nonzero Temperature in a Disordered Dipolar Ising System: The Case of LiHoxY{1-x}F4

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.