Uniformly Frustrated XY Model without a Vortex-Pattern Ordering

The uniformly frustrated XY model with f=1/3 on a dice lattice is shown to possess an accidental degeneracy of its ground states so well developed that the difference between the free energies of fluctuations does not lead to the stabilization of a particular vortex pattern down to zero temperature. Nonetheless, at low temperatures the system is characterized by a finite helicity modulus whose vanishing (at a finite temperature) is related to the dissociation of half-vortex pairs.