  The main aim of the present work is to analyse the effect of dipolar
interaction strength $\lambda$, particle size $D$ and temperature $T$ on the
hysteresis mechanism in ordered arrays of magnetic nanoparticles (MNPs) using
computer simulations. The anisotropy axes of the MNPs are assumed to have
random orientation to mimic the real system. In the absence of thermal
fluctuations and dipolar interaction, the hysteresis follows the Stoner and
Wohlfarth model irrespective of $D$, as expected. The hysteresis loop area is
minimal for particle sizes $D \approx8-16$ nm at $T=300$ K and $\lambda=0.0$,
indicating the dominance of superparamagnetic character. Switching magnetic
interaction on is able to move the MNPs from superparamagnetic to a
ferromagnetic state even at room temperature; therefore, magnetic interaction
of enough strength enhances the hysteresis loop area. Interestingly, the
hysteresis loop area is significant and is the same as that of Stoner and
Wohlfarth particle even $T=300$ K and negligible dipolar interaction for
ferromagnetic MNPs ($D>16$ nm). The coercive field $\mu^{}_oH^{}_c$ and
blocking temperature $T^{}_B$ also get enhanced with an increase in $\lambda$
and $D$. The rigorous analysis of the coercive field $\mu^{}_oH^{}_c$ vs
temperature data also reveals significant deviation from $T^{3/4}$ dependence
of $\mu^{}_oH^{}_c$ because of dipolar interaction. The amount of heat
dissipated $E^{}_H$ and $\mu_oH^{}_c$ decrease rapidly with $T$ for $D\approx
8-16$ nm and $\lambda\leq0.6$. On the other hand, $E^{}_H$ and $\mu^{}_oH^{}_c$
depend weakly on $T$ with $D>16$ nm, even in the weak dipolar limit. The
present work should provide a better understanding of magnetic hyperthermia to
researchers working on this subject. For physicists, it would be interesting to
test experimentally the results described in this article.
