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 $T_0$ from Monte Carlo simulations. Simple empirical relations, which give $T_0$ for simple and body-centered tetragonal lattices in terms of lattice parameters, are also established. Finally, the nature of the ordered state and $T_0$ are determined for ${\mathrm{Fe}}_8$ clusters, which crystallize on a triclinic lattice.

• Received 2 February 2000

DOI:https://doi.org/10.1103/PhysRevB.62.53