Study of the de Almeida–Thouless line in the one-dimensional diluted power-law vector spin glass

We study the de Almeida–Thouless (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^2σ. Tuning the exponent σ is equivalent to changing the space dimension of a short-range model. 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. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. We also have large-scale Monte Carlo simulations for the Heisenberg version of the power-law diluted spin-glass model, which show broad agreement with our results for the XY spin glass model.