  Finite-size and surface effects in fine particle systems are investigated by
Monte Carlo simulation of a model of a $\gamma$-Fe$_2$O$_3$ (maghemite) single
particle. Periodic boundary conditions have been used to simulate the bulk
properties and the results compared with those for a spherical shaped particle
with free boundaries to evidence the role played by the surface on the
anomalous magnetic properties displayed by these systems at low temperatures.
Several outcomes of the model are in qualitative agreement with the
experimental findings. A reduction of the magnetic ordering temperature,
spontaneous magnetization, and coercive field is observed as the particle size
is decreased. Moreover, the hysteresis loops become elongated with high values
of the differential susceptibility, resembling those from frustrated or
disordered systems. These facts are consequence of the formation of a surface
layer with higher degree of magnetic disorder than the core, which, for small
sizes, dominates the magnetization processes of the particle. However, in
contradiction with the assumptions of some authors, our model does not predict
the freezing of the surface layer into a spin-glass-like state. The results
indicate that magnetic disorder at the surface simply facilitates the thermal
demagnetization of the particle at zero field, while the magnetization is
increased at moderate fields, since surface disorder diminishes ferrimagnetic
correlations within the particle. The change in shape of the hysteresis loops
with the particle size demonstrates that the reversal mode is strongly
influenced by the reduced atomic coordination and disorder at the surface.
