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We test for the presence or absence of the de Almeida-Thouless line usingone-dimensional power-law diluted Heisenberg spin glass model, in which the rmsstrength of the interactions decays with distance, r as 1/r^{sigma}. It isargued that varying the power sigma is analogous to varying the space dimensiond in a short-range model. For sigma=0.6, which is in the mean field regimeregime, we find clear evidence for an AT line. For sigma = 0.85, which is inthe non-mean-field regime and corresponds to a space dimension of close to 3,we find no AT line, though we cannot rule one out for very small fields.Finally for sigma=0.75, which is in the non-mean-field regime but closer to themean-field boundary, the evidence suggests that there is an AT line, though thepossibility that even larger sizes are needed to see the asymptotic behaviorcan not be ruled out.

Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses