Study of metastable states in the random-field Ising model

The random-field Ising model (RFIM) provides a convenient framework to investigate complex energy landscapes. We use an out-of-equilibrium T ¼ 0 single spin flip dynamics induced by varying the applied field, starting from locally stable configurations fsi g: If the configuration considered cannot be reached by a field history from saturation, it is possible to define a set of connected states which is defined as a basin. A whole hierarchy of basins is found when the field is increased outside the limits of the initial basin. The resulting structure has the topology of an oriented graph. The properties of the graph cast new light on properties of the ground state (GS) and the possibility to reach the GS by a field history from saturation. We have numerically determined the graphs in RFIM realizations of finite size in one dimension for arbitrary selected states and for the GS. Remarkable differences between them are found in the critical path of the corresponding graphs, the GS being nearer to the field reachable states than a generic state.