Continuous ground-state degeneracy of classical dipoles on regular lattices

Dipolar interactions are crucial in the modeling of many complex magnetic systems, such as the pyrochlores and artificial spin systems. Remarkably, many classical dipolar coupled spin systems exhibit a continuous ground-state degeneracy, which is unexpected as the Hamiltonian does not possess a continuous symmetry. In this paper, we explain, how such a finite point-symmetry leads to a continuous ground-state degeneracy of specific classical dipolar-coupled systems. This work, therefore, provides new insight into the theory of classical dipolar-coupled spin-systems and opens the way to understand more complex dipolar coupled systems.