  We investigated the effect of intermolecular dipolar interactions on a cubic
3D ensemble of 5X5X4=100 nanomagnets, each with spin $S = 5$. We employed the
Landau-Lifshitz-Gilbert equation to solve for the magnetization $M(B)$ curves
for several values of the damping constant $\alpha$, the induction sweep rate,
the lattice constant $a$, the temperature $T$, and the magnetic anisotropy
field $H_A$. We find that the smaller the $\alpha$, the stronger the maximum
induction required to produce hysteresis. The shape of the hysteresis loops
also depends on the damping constant. We find further that the system
magnetizes and demagnetizes at decreasing magnetic field strengths with
decreasing sweep rates, resulting in smaller hysteresis loops. Variations of
$a$ within realistic values (1.5 nm - 2.5 nm) show that the dipolar interaction
plays an important role in the magnetic hysteresis by controlling the
relaxation process. The $T$ dependencies of $\alpha$ and of $M$ are presented
and discussed with regard to recent experimental data on nanomagnets. $H_A$
enhances the size of the hysteresis loops for external fields parallel to the
anisotropy axis, but decreases it for perpendicular external fields. Finally,
we reproduce and test an $M(B)$ curve for a 2D-system [M. Kayali and W. Saslow,
Phys. Rev. B {\bf 70}, 174404 (2004)]. We show that its hysteretic behavior is
only weakly dependent on the shape anisotropy field and the sweep rate, but
depends sensitively upon the dipolar interactions. Although in 3D systems,
dipole-dipole interactions generally diminish the hysteresis, in 2D systems,
they strongly enhance it. For both square 2D and rectangular 3D lattices with
${\bm B}||(\hat{\bm x}+\hat{\bm y})$, dipole-dipole interactions can cause
large jumps in the magnetization.
