Local excitations of a spin glass in a magnetic field

We study the minimum energy clusters (\textsc{mec}) above the ground state for the $3-d$ Edwards-Anderson spin glass in a magnetic field. For fields $B$ below 0.4, we find that the field has almost no effect on the excitations that we can probe, of volume $V \leq 64$. As found for B=0, their energies decrease with $V$, and their magnetization remains very small (even slightly negative). For larger fields, both the \textsc{mec} energy and magnetization grow with $V$, as expected in a paramagnetic phase. However, all results appear to scale as $BV$ (instead of $B \sqrt{V}$ as expected from droplet arguments), suggesting that the spin glass phase is destroyed by any small field. Finally, the geometry of the \textsc{mec} is completely insensitive to the field, giving further credence that they are lattice animals even in the absence of a field.