Fluctuation-induced vortex pattern and its disordering in the fully frustratedXYmodel on a dice lattice

Abstract

A highly degenerate family of states, in which the adjacent plaquettes with the same sign of vorticity form clusters of three [proposed in Phys. Rev. B 63, 134503 (2001)], is proven to really minimize the Hamiltonian of the fully frustrated $XY$ model on a dice lattice. The harmonic fluctuations are demonstrated to be of no consequence for the removal of the accidental degeneracy of these states, so a particular vortex pattern can be stabilized only by the anharmonic fluctuations. The structure of this pattern is found and the temperature of its disordering due to the proliferation of domain walls is estimated. The extreme smallness of the fluctuation-induced free energy of domain walls leads to the anomalous prominence of the finite-size effects, which prevents the observation of vortex-pattern ordering in numerical simulations. In such circumstances the loss of phase coherence may be related to the dissociation of pairs of fractional vortices with the topological charges $\ifmmode\pm\else\textpm\fi{}1∕8$. In a physical situation the magnetic interactions of currents in a Josephson junction array will be a more important source for the stabilization of a particular vortex pattern then the anharmonic fluctuations.