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

Abstract

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 $1/{r}^{\ensuremath{\sigma}}$. It is argued that varying the power $\ensuremath{\sigma}$ is analogous to varying the space dimension $d$ in a short-range model. For $\ensuremath{\sigma}=0.6$, which is in the mean-field regime regime, we find clear evidence for an AT line. For $\ensuremath{\sigma}=0.85$, 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 $\ensuremath{\sigma}=0.75$, 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.