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 $N=2... 13$. 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 $N=3... 6$. The area $A_N$ of the hysteresis loop is studied as a function of $N$. We find that $A_N-A_\infty$ approximately scales as $N^{-{3/2}}$ for $N$ odd and as $N^{-2}$ for $N$ even.