Vortex ordering in fully frustrated superconducting systems with a dice lattice

The structure and the degeneracy of the ground state of a fully frustrated $\mathrm{XY}$ model are investigated for the case of a dice-lattice geometry. The results are applicable for the description of Josephson junction arrays and thin superconducting wire networks in the external magnetic field providing half-integer number of flux quanta per plaquette. The mechanisms of disordering of vortex pattern in such systems are briefly discussed.