Dynamical-system theory approach to the study of metastable states in the random field Ising model

In this paper, we obtain information about the topological structure of the energy landscape of the random-field Ising model by numerical simulations. We define and construct a suitable map (one-loop map) for the representation of generic metastable state. We show that the properties of this map are strictly related to the possibility of generating the state by a field history.