  We study the magnetic hysteresis in the random field Ising model in 3D. We
discuss the disorder dependence of the coercive field H_c, and obtain an
analytical description of the smooth part of the hysteresis below and above
H_c, by identifying the disorder configurations (instantons) that are the most
probable to trigger local avalanches. We estimate the critical disorder
strength at which the hysteresis curve becomes continuous. From an instanton
analysis at zero field we obtain a description of local two-level systems in
the ferromagnetic phase.
