  We study the ground state and magnetic hysteresis properties of 2$d$ arrays
($L^{}_x\times L^{}_y$) of dipolar interacting magnetic nanoparticles (MNPs) by
performing micromagnetic simulations. Our primary interest is to understand the
effect of sample shape, $\Theta$- the ratio of the dipolar strength to the
anisotropy strength, and the direction of the applied field $\vec{H} =
H_{o}\hat{e}^{}_H$ on the ground state and the magnetic hysteresis in an array
of MNPs. To study the effect of shape of the sample, we have varied the aspect
ratio $A^{}_r=L^{}_y/L^{}_x$ which in turn, is found to induce shape anisotropy
in the system. Our main observations are: (a) When the dipolar interaction is
strong $(\Theta>1)$, the ground state morphology has in-plane ordering of
magnetic moments. (b) The ground state morphology has randomly oriented
magnetic moments which is robust with respect to system sizes and $A^{}_r$ for
weakly interacting MNPs ($\Theta<1$). (c) Micromagnetic simulations suggests
that the dipolar interaction decreases the coercive field $H^{}_c$. (d) The
remanence magnetization $M^{}_r$ is found to be strongly dependent not only on
the strength of dipolar interaction but also on the shape of the sample. (e)
Due to anisotropic nature of dipolar interaction, a strong effect of shape
anisotropy is observed when the field is applied along longer axis of the
sample. The dipolar interaction in such a case induces an effective
ferromagnetic coupling when the aspect ratio is very large. These results are
of vital importance in high-density recording systems, magneto-impedance
sensors, etc.
