Ground states of a frustrated kagomé array of Josephson junctions

We study the ground state vortex lattices of a kagomé array of Josephson junctions in an external magnetic field. We give a simple model that accounts for the principal dependence of ground state energy on the density of vortices, and exhibit the exact ground state configurations for a sequence of special values. A Monte Carlo simulated annealing shows that there is very little further structure. For the special case (formula presented) it is known that there is an infinite degeneracy. We give a numerical technique for evaluating the zero temperature entropy.