Study of the de Almeida-Thouless line using power-law diluted one-dimensional Heisenberg spin glasses

In a recent study, we showed that in mean-field theory, there is a de Almeida-Thouless (AT) line, that separates the low-temperature, low-field spin-glass phase from a high-temperature, high-field paramagnetic phase, for arbitrary $m$-component vector spin glasses, provided one applies a magnetic field that is \emph{random in direction.} Building on this piece of work, here, we investigate whether or not there is an AT line beyond mean-field theory for Heisenberg spin glasses by performing Monte Carlo simulations on a power-law diluted one-dimensional Heisenberg spin glass for very large system sizes.