  This chapter is aimed at studying the anomalous magnetic properties (glassy
behaviour) observed at low temperatures in nanoparticles of ferrimagnetic
oxides. This topic is discussed both from numerical results and experimental
data. Ferrimagnetic fine particles show most of the features of glassy systems
due to the random distribution of anisotropy axis, interparticle interactions
and surface effects. Experiments have shown that the hysteresis loops display
high closure fields with high values of the differential susceptibility. Low
magnetisation as compared to bulk, shifted loops after field-cooling, highfield
irreversibilities between zero-field and field cooling processes and ageing
phenomena in the time-dependence of the magnetisation, are also observed. This
phenomenology indicates the existence of some kind of freezing phenomenon
arising from a complex hierarchy of the energy levels, whose origin is
currently under discussion. Two models have been proposed to account for it: i)
the existence of a spin-glass state at the surface of the particle which is
coupled to the particle core through an exchange field; and ii) the collective
behaviour induced by interparticle interactions. In real systems, both
contributions simultaneously occur, being difficult to distinguish their
effects. In contrast, numerical simulations allow us to build a model just
containing the essential ingredients to study solely one of two phenomena.
