  The magnetization curves of densely packed single domain magnetic
nanoparticles (MNP) are investigated by Monte Carlo simulations in the
framework of an effective one spin model. The particles whose size
polydispersity is taken into account are arranged in spherical clusters and
both dipole dipole interactions (DDI) and magnetic anisotropy energy (MAE) are
included in the total energy. Having in mind the special case of spinel
ferrites of intrinsic cubic symmetry, combined cubic and uniaxial
magnetocrystalline anisotropies are considered with different configurations
for the orientations of the cubic and uniaxial axes. It is found that the DDI,
together with a marked reduction of the linear susceptibility are responsible
for a damping of the peculiarities due to the MAE cubic component on the
magnetization. As an application, we show that the simulated magnetization
curves compare well to experimental results for $\gamma$--Fe$_2$O$_3$ MNP for
small to moderate values of the field.
