Local excitations of a spin glass in a magnetic field

We study the minimum energy clusters (MEC) above the ground state for the $3-d$ Edwards-Anderson Ising 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 $V<~64.$ As found previously for $B=0,$ their energies decrease with V, and their magnetization remains very small (even slightly negative). For larger fields, both the MEC energy and magnetization grow with V, as expected in a paramagnetic phase. However, all results appear to scale as $\mathrm{BV}$ (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 MEC is completely insensitive to the field, giving further credence that they are lattice animals, in the presence or the absence of a field.