  In this work, we study the effect of dipole-dipole interparticle interactions
on the static thermodynamic and magnetic properties of an ensemble of
immobilized monodisperse superparamagnetic nanoparticles. We assume that
magnetic nanoparticles are embedded in the nodes of a regular cubic lattice, so
that the particle translational degrees of freedom are turned off. The
relaxation of the magnetic moments of the nanoparticles occurs by the Neel
mechanism. The easy axes are aligned (i) parallel or (ii) perpendicular to the
direction of an external field. These models are investigated using theory and
computer simulation, taking microscopic discrete structure explicitly into
account. The analytical expressions of the Helmholtz free energy, the static
magnetization, and the initial magnetic susceptibility are derived for both
configurations (i) and (ii) as functions of the height of the magnetic
crystallographic anisotropy energy barrier, measured by parameter $\sigma$, and
the intensity of the dipole-dipole interparticle interactions measured by
$\lambda_e$. A good agreement between the theory and the results of MC
simulations in the region of low and moderate values of $\lambda_e$ and
$\sigma$ is obtained. For high values of $\lambda_e$ and $\sigma$, the
structuring of magnetic moments in regularly orientated structures was found
from MC simulations for configuration (i).
