Hysteresis of Finite Arrays of Magnetic nano Dots

Hysteresis curves for finite arrays of $N\times N$ ferromagnetic nano dots subject to the dipole-dipole interaction are investigated for $N=\mathrm{2...13}$. Spin arrangements up to N=6 are presented, which indicate the onset of bulk-like behavior associated with odd (N=5) and even (N=6) systems. The effect of field misalignment on the hysteresis loops is also studied for $N=\mathrm{3...6}$. The area $A_N$ of the hysteresis loop is studied as a function of $N$. We find that $A_N-A_{\mathrm{\infty }}$ approximately scales as $N^{-3\mathrm{/}2}$ for $N$ odd and as $N^{-2}$ for $N$ even.