  The low temperature behavior of densely packed interacting spherical single
domain nanoparticles (MNP) is investigated by Monte Carlo simulations in the
framework of an effective one spin model. The particles are distributed through
a hard sphere like distribution with periodic boundary conditions and interact
through the dipole dipole interaction (DDI) with an anisotropy energy including
both cubic and uniaxial symmetry components. The cubic component is shown to
play a sizable role on the value of the blocking temperature $T_b$ only when
the MNP easy axes are parallel to the cubic easy direction ([111] direction for
a negative cubic anisotropy constant). The nature of the collective low
temperature state, either ferromagnetic or spin glass like, is found to depend
on the ratio of the anisotropy to the dipolar energies characterizing partly
the disorder in the system.
