  We present a numerical simulation study of the exchange bias (EB) effect in
nanoparticles with core/shell structure aimed to unveil the microscopic origin
of some of the experimental phenomenology associated to this effect. In
particular, we have focused our study on the particle size and field cooling
dependence of the hysteresis loop shifts. To this end, hysteresis loops after a
field cooling process have been computed by means of Monte Carlo simulations
based on a model that takes into account the peculiar properties of the core,
shell and interfacial regions of the particle and the EB and coercive fields
have been extracted from them. The results show that, as a general trend, the
EB field $h_{EB}$ decreases with increasing particle size, in agreement with
some experimental observations. However, closer inspection reveals notable
oscillations of $h_{EB}$ as a function of the particle radius which we show to
be closely related to the net magnetization established after field cooling at
the interfacial shell spins. For a particle with ferromagnetic interface
coupling, we show that the magnitude and sign of $h_{EB}$ can be varied with
the magnetic field applied during the cooling process.
