%0 Journal Article
%T Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems
%A Juan Carlos Andresen
%A Helmut G. Katzgraber
%A Vadim Oganesyan
%A Moshe Schechter
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevX.4.041016
%X The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin-glasses are subject of controversy and ongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration 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 with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all Ho ion concentrations down to the smallest concentration numerically accessible of 0.1%, and including Ho ion concentrations which coincide with those studied experimentally up to 16.7%. Our results suggest that randomly-diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration, in agreement with mean field theory.
%U http://arxiv.org/abs/1407.4782v2