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An infinite triangular lattice of classical dipolar spins is usuallyconsidered to have a ferromagnetic ground state. We examine the validity ofthis statement for finite lattices and in the limit of large lattices. We findthat the ground state of rectangular arrays is strongly dependent on size andaspect ratio. Three results emerge that are significant for understanding theground state properties: i) formation of domain walls is energetically favoredfor aspect ratios below a critical valu e; ii) the vortex state is alwaysenergetically favored in the thermodynamic limit of an infinite number ofspins, but nevertheless such a configuration may not be observed even in verylarge lattices if the aspect ratio is large; iii) finite range approximationsto actual dipole sums may not provide the correct ground sta te configurationbecause the ferromagnetic state is linearly unstable and the domain wall energyis negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as  a Rapid Communication in Phys. Rev.

Dipolar ground state of planar spins on triangular lattices