Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass

Understand

We study the AT line in the one-dimensional power-law diluted XY spin glass model, in which the probability that two spins separated by a distance $r$ interact with each other, decays as $1/r^{2\sigma}$.

• We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large scale Monte Carlo simulations.
• For $\sigma=0.6$ which is in the mean-field regime, we find clear evidence for an AT line.
• For $\sigma = 0.75$, there is evidence from finite size scaling studies for an AT transition but for $\sigma = 0.85$, the evidence for a transition is non-existent.