Numerical study of metastable states in the T=0 RFIM

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.