On the ordering of Ising spin glasses in a field

We study the existence of a spin-glass phase in a magnetic field in three space dimensions using a novel approach where the Monte Carlo simulations are performed along a nontrivial path in the magnetic field--temperature plane which must cross any putative de Almeida-Thouless line. The method is first tested on the mean-field version of the Edwards-Anderson Ising spin glass on a Bethe lattice where we compute analytically the instability line that separates the spin glass from the paramagnetic state. While the de Almeida-Thouless line is clearly reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model. We thus conclude that there is no such instability line for three-dimensional short-range Ising spin glasses.