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

TL;DR

This study investigates the existence of the de Almeida-Thouless line in a one-dimensional power-law diluted Heisenberg spin glass model, revealing its presence in the mean-field regime and absence in the non-mean-field regime near three dimensions.

Contribution

It demonstrates how varying the power-law decay parameter sigma simulates different effective dimensions and examines the AT line's presence across these regimes.

Findings

AT line present at sigma=0.6 (mean-field regime)

No AT line detected at sigma=0.85 (near 3D non-mean-field)

Possible AT line at sigma=0.75, but larger sizes may be needed

Abstract

We test for the presence or absence of the de Almeida-Thouless 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^{sigma}. It is argued that varying the power sigma is analogous to varying the space dimension d in a short-range model. For sigma=0.6, which is in the mean field regime regime, we find clear evidence for an AT line. For 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 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.