  We investigate the effect of anisotropy and weak dipolar interactions on the
magnetization of an assembly of nanoparticles with distributed magnetic
moments, i.e., assembly of magnetic nanoparticles in the one-spin
approximation, with textured or random anisotropy.
  The magnetization of a free particle is obtained either by a numerical
calculation of the partition function or analytically in the low and high field
regimes, using perturbation theory and the steepest-descent approximation,
respectively. The magnetization of an interacting assembly is computed
analytically in the range of low and high field, and numerically using the
Monte Carlo technique.
  Approximate analytical expressions for the assembly magnetization are
provided which take account of the dipolar interactions, temperature, magnetic
field, and anisotropy. The effect of anisotropy and dipolar interactions are
discussed and the deviations from the Langevin law they entail are
investigated, and illustrated for realistic assemblies with the lognormal
moment distribution.
