  Ground states of the three dimensional Edwards-Anderson spin glass are
computed in the presence of an external magnetic field. Our algorithm is
sufficiently powerful for us to treat systems with up to 600 spins. We perform
a statistical analysis of how the ground state changes as the field is
increased, and reach the conclusion that the spin glass phase at zero
temperature does not survive in the presence of any finite field. This is in
agreement with the droplet model or scaling predictions, but in sharp
disagreement with the mean field picture. For comparison, we also investigate a
dilute mean field spin glass model where an Almeida-Thouless line is present.
