The dipole-dipole potential in statistical mechanics

We study the interaction energy of a system of N particles with embedded point dipoles in a cube, this cube being duplicated indefinitely throughout space. We are able to evaluate exactly this energy for arbitrary positions and orientations of the N particles, to provide an effective hamiltonian suitable for the study of the statistical mechanics of dipolar systems by both rigorous methods and computer simulation techniques. We describe methods for the rapid numerical evaluation of the hamiltonian and how it may be employed for the tasks outlined above.