  Dipole-dipole interactions in a square planar array of sub-micron magnetic
disks (magnetic dots) have been studied theoretically. Under a normal magnetic
field the ground-state of the array undergoes many structural transitions
between the limiting chessboard antiferromagnetic state at zero field and the
ferromagnet at a threshold field. At intermediate fields, numerous
ferrimagnetic states having mean magnetic moments between zero and that of the
ferromagnetic state are favorable energetically. The structures and energies of
a selection of states are calculated and plotted, as are the fields required to
optimally reverse the magnetic moment of a single dot within them. Approximate
formulae for the dipolar energy and anhysteretic magnetization curve are
presented.
