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The nature of ordering in dilute dipolar interacting systems dates back tothe work of Debye and is one of the most basic, oldest and as-of-yet unsettledproblems in magnetism. While spin-glass order is readily observed in severalRKKY-interacting systems, dipolar spin-glasses are subject of controversy andongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomlydiluted uniaxial (Ising) dipolar system. In particular, it is unclear if thespin-glass phase in these paradigmatic materials persists in the limit of zeroconcentration or not. We study an effective model of ${{\rm LiHo_xY_{1-x}F_4}}$using large-scale Monte Carlo simulations that combine parallel tempering witha special cluster algorithm tailored to overcome the numerical difficultiesthat occur at extreme dilutions. We find a paramagnetic to spin-glass phasetransition for all Ho ion concentrations down to the smallest concentrationnumerically accessible of 0.1%, and including Ho ion concentrations whichcoincide with those studied experimentally up to 16.7%. Our results suggestthat randomly-diluted dipolar Ising systems have a spin-glass phase in thelimit of vanishing dipole concentration, with a critical temperature vanishinglinearly with concentration, in agreement with mean field theory.

Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems