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 relat ion provides insight into the relation between lattice geometry and the nat ure of the ordered state. It can be used to calculate ground-state energies . We have also obtained ground-state energies and ordering temperatures T-0 from Monte Carlo simulations. Simple empirical relations, which give T-0 f or simple and body-centered tetragonal lattices in terms of lattice paramet ers, are also established. Finally, the nature of the ordered state and T-0 are determined for Fe-8 clusters, which crystallize on a triclinic lattice .