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).
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