We study numerically the number of single-spin-flip stable states in the T=0 random field Ising model 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.
Perez-Reche, F. J., Rosinberg, M. L., & Tarjus, G. (2008). Numerical approach to metastable states in the zero-temperature random-field Ising model. Physical Review B, 77(6), . https://doi.org/10.1103/PhysRevB.77.064422