2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228838We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally-applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that an Almeida-Thouless line only occurs in the mean field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.4 pages, 2 figures, 1 tableDisordered Systems and Neural Networkstext