Ordering of dipolar Ising crystals

We study Ising systems of spins with dipolar interactions. We find a simple approximate relation for the interaction energy between pairs of parallel lattice columns of spins running along the Ising spin direction. This relation provides insight into the relation between lattice geometry and the nature of the ordered state. It can be used to calculate ground-state energies. We have also obtained ground-state energies and ordering temperatures T₀ from Monte Carlo simulations. Simple empirical relations, which give T₀ for simple and body-centered tetragonal lattices in terms of lattice parameters, are also established. Finally, the nature of the ordered state and T₀ are determined for Fe₈ clusters, which crystallize on a triclinic lattice.