  A detailed numerical simulation of quasistatic hysteresis loops of dense
clusters of interacting magnetic nanoparticles is carried out. Both clusters of
magnetically soft and magnetically hard nanoparticles are considered. The
clusters are characterized by an average particle diameter D, the cluster
radius Rc, the particle saturation magnetization Ms, and the uniaxial
anisotropy constant K. The number of particles in the cluster varies between Np
= 30 - 120. The particle centers are randomly distributed within the cluster,
their easy anisotropy axes being randomly oriented. It is shown that a rare
assembly of identical random clusters of magnetic nanoparticles can be
characterized by two dimensionless parameters: 1) the relative strength of
magneto-dipole interaction, K/Ms^2, and the average particle concentration
within the cluster, {\eta} = VNp/Vc. Here V is the nanoparticle volume, and Vc
is the volume of the cluster, respectively. In the strong interaction limit,
Ms*{\eta}/Ha >> 1, where Ha = 2K/Ms is the anisotropy field, the ultimate
hysteresis loops of dilute assemblies of clusters have been constructed. In the
variables (M/Ms, H/Ms) these hysteresis loops depend only on the particle
volume fraction {\eta}. In the weak interaction limit, Ms*{\eta}/Ha << 1, the
assembly hysteresis loops in the variables (M/Ms, H/Ha) are close to the
standard Stoner-Wohlfarth hysteresis loop.
