We analyze low field hysteresis close to the demagnetized state in disordered
ferromagnets using the zero temperature random-field Ising model. We solve the
demagnetization process exactly in one dimension and derive the Rayleigh law of
hysteresis. The initial susceptibility a and the hysteretic coefficient b
display a peak as a function of the disorder width. This behavior is confirmed
by numerical simulations d=2,3 showing that in limit of weak disorder
demagnetization is not possible and the Rayleigh law is not defined. These
results are in agreement with experimental observations on nanocrystalline
magnetic materials.Comment: Extended version, 18 pages, 5 figures, to appear in Phys. Rev.
