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.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.

arXiv:1105.1352Physical Review BJul 28, 201116 citations

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.