  An infinite triangular lattice of classical dipolar spins is usually
considered to have a ferromagnetic ground state. We examine the validity of
this statement for finite lattices and in the limit of large lattices. We find
that the ground state of rectangular arrays is strongly dependent on size and
aspect ratio. Three results emerge that are significant for understanding the
ground state properties: i) formation of domain walls is energetically favored
for aspect ratios below a critical valu e; ii) the vortex state is always
energetically favored in the thermodynamic limit of an infinite number of
spins, but nevertheless such a configuration may not be observed even in very
large lattices if the aspect ratio is large; iii) finite range approximations
to actual dipole sums may not provide the correct ground sta te configuration
because the ferromagnetic state is linearly unstable and the domain wall energy
is negative for any finite range cutoff.
