Surface and bulk energies of dipolar lattices

We calculate the field due to lines and planes of dipoles, and use this to calculate the bulk and surface energies of various dipolar-lattice structures. The calculation technique is simpler than traditional Ewald methods, and is well suited to surface-energy calculations. We find strongly anisotropic surface energies for the lattices; the more closely packed lattices have negative surface energies for directions approximately parallel to the dipolar axis. These results should be applicable to ferro- and electrorheological fluids.