  We perform computer simulations to probe the magnetic hysteresis in a
two-dimensional ($L^{}_x\times L^{}_y$) assembly of magnetic nanoparticles as a
function of dipolar interaction strength $h^{}_d$, temperature $T$, aspect
ratio $A^{}_r=L^{}_y/L^{}_x$, and the applied alternating magnetic field's
direction. In the absence of magnetic interaction ($h^{}_d\approx0$) and
thermal fluctuations ($T=0$ K), the hysteresis follows the Stoner and Wohlfarth
model, as expected. For weak dipolar interaction and substantial temperature,
the hysteresis has the dominance of superparamagnetic behaviour, irrespective
of the applied magnetic field's direction and $A^{}_r$. Interestingly, the
hysteresis curve has all the characteristics of antiferromagnetic interaction
dominance for $A^{}_r\leq6$ and considerable dipolar interaction strength
($h^{}_d>0.2)$, which is independent of applied magnetic direction. When the
magnetic field is applied along the system's shorter axis ($x$-direction), a
non-hysteresis straight line is observed with large $h^{}_d$. In the case of
the magnetic field applied along the long axis of the sample ($y$-direction),
ferromagnetic interaction dominates the hysteresis for large $h^{}_d$ and
$A^{}_r>6$. Irrespective of $h^{}_d$ and applied magnetic field's direction,
the coercive field $\mu^{}_oH^{}_c$ and remanence $M^{}_r$ are minimal for
$A^{}_r\leq6$ and significant temperature. They are found to increase with
$h^{}_d$ when $A^{}_r$ is enormous. Remarkably, the variation of hysteresis
loop area $E^{}_H$ as a function of these parameters is the same as that of the
coercive field variation. We believe that the concepts presented in this work
are relevant in various technological applications such as spintronics and
magnetic hyperthermia, in which such self-assembled nanoparticle arrays are
ubiquitous.
