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

• Published in: arXiv.org
• Main Authors: Andresen, Juan Carlos, Katzgraber, Helmut G, Oganesyan, Vadim, Schechter, Moshe
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 28.10.2014
• Subjects: Algorithms; Computer simulation; Critical temperature; Dilution; Dipoles; Ising model; Magnetism; Mathematical models; Mean field theory; Phase transitions; Physics - Disordered Systems and Neural Networks; Physics - Materials Science; Rare earth elements; Spin glasses
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1407.4782

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.