  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.
