de Almeida–Thouless line studied using one-dimensional power-law diluted Heisenberg spin glasses

We test for the presence or absence of the de Almeida--Thouless (AT) line using one-dimensional power-law diluted Heisenberg spin-glass model, in which the rms strength of the interactions decays with distance, r as 1/r^σ. It is argued that varying the power σ is analogous to varying the space dimension d in a short-range model. For σ=0.6, which is in the mean-field regime regime, we find clear evidence for an AT line. For σ=0.85, which is in the 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 σ=0.75, which is in the non-mean-field regime but closer to the mean-field boundary, the evidence suggests that there is an AT line, though the possibility that even larger sizes are needed to see the asymptotic behavior can not be ruled out.