  We study numerically the number of single-spin-flip stable states in the T=0
Random Field Ising Model (RFIM) on random regular graphs of connectivity $z=2$
and $z=4$ and on the cubic lattice. The annealed and quenched complexities
(i.e. the entropy densities) of the metastable states with given magnetization
are calculated as a function of the external magnetic field. The results show
that the appearance of a (disorder-induced) out-of-equilibrium phase transition
in the magnetization hysteresis loop at low disorder can be ascribed to a
change in the distribution of the metastable states in the field-magnetization
plane.
