  Monte Carlo simulations of a model for $\gamma$-Fe$_2$O$_3$ (maghemite)
single particle of spherical shape are presented aiming at the elucidation the
specific role played by the finite size and the surface on the anomalous
magnetic behaviour observed in small particle systems at low temperature. The
influence of the finite-size effects on the equilibrium properties of extensive
magnitudes, field coolings and hysteresis loops is studied an compared to the
results for periodic boundaries. It is shown that for the smallest sizes the
thermal demagnetization of the surface completely dominates the magnetization
while the behaviour of the core is similar to that of the periodic boundary
case, independently of $D$. The change in shape of the hysteresis loops with
$D$ demonstrates that the reversal mode is strongly influenced by the presence
of broken links and disorder at the surface.
