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In this work, we study the effect of dipole-dipole interparticle interactionson the static thermodynamic and magnetic properties of an ensemble ofimmobilized monodisperse superparamagnetic nanoparticles. We assume thatmagnetic nanoparticles are embedded in the nodes of a regular cubic lattice, sothat the particle translational degrees of freedom are turned off. Therelaxation of the magnetic moments of the nanoparticles occurs by the Neelmechanism. The easy axes are aligned (i) parallel or (ii) perpendicular to thedirection of an external field. These models are investigated using theory andcomputer simulation, taking microscopic discrete structure explicitly intoaccount. The analytical expressions of the Helmholtz free energy, the staticmagnetization, and the initial magnetic susceptibility are derived for bothconfigurations (i) and (ii) as functions of the height of the magneticcrystallographic anisotropy energy barrier, measured by parameter $\sigma$, andthe intensity of the dipole-dipole interparticle interactions measured by$\lambda_e$. A good agreement between the theory and the results of MCsimulations in the region of low and moderate values of $\lambda_e$ and$\sigma$ is obtained. For high values of $\lambda_e$ and $\sigma$, thestructuring of magnetic moments in regularly orientated structures was foundfrom MC simulations for configuration (i).

Thermodynamics of interacting single-domain superparamagnetic nanoparticles frozen in the nodes of a regular cubic lattice