The Distribution of Multiple Energy Minima and Hysteresis in Zero   Temperature Random Field Ising Model
  The Random Field Ising Model (RFIM) is the simplest physical model reflecting effect of quenched disorder on the different types of phase transitions in solids. The presence of multiple energy minima in the RFIM is an important feature determining main physical properties of the systems with a field type of quenched disorder. In particular, according to computer simulations of Sethna at al. performed for a zero temperature RFIM, the irreversible loop of magnetization appears as direct result of their presence. In the present paper the analytic method based on the total number of energy minima estimation is developed to study the hysteretic behavior of a zero temperature RFIM. As a result, the magnetization hysteresis loop is obtained as a marginal curve separating metastable and completely unstable states in the magnetization-external field plane. 
A.A. Likhachev