  A model consisting of random interacting anti-ferromagnetic (AF) grains
coupled to a ferromagnetic (FM) layer is developed to study the exchange bias
phenomenon. This simple model is able to describe several exchange bias
behavior observed in real materials. Shifts in hysteresis loops are observed as
a function of cooling field and average grain size. We establish a direct
relationship between cooling field dependence of exchange bias, coercivity and
magnetization state on the AF-FM interface. We also verify that the exchange
bias field is inversely proportional to the grain size, and this behavior is
independent of the inter-grain interactions, AF/FM coupling and cooling field.
