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We test for the existence of a spin-glass phase transition, the de AlmeidaâThouless 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 a de AlmeidaâThouless line occurs only in the mean-field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.
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