Ordered phases and phase transitions in the fully frustratedXYmodel on a honeycomb lattice

Abstract

The phase diagram of the fully frustrated $XY$ model on a honeycomb lattice is shown to incorporate three different ordered phases. In the most unusual of them, a long-range order is related not to the dominance of a particular periodic vortex pattern but to the orientation of the zero-energy domain walls separating domains with different orientations of vortex stripes. The phase transition leading to the destruction of this phase can be associated with the appearance of free fractional vortices and is of the first order. The stabilization of the two other ordered phases (existing at lower temperatures) relies on a positive contribution to the domain-wall free energy induced by the presence of spin waves. This effect has a substantial numerical smallness, in accordance with which these two phases can be observed only in the systems of really macroscopic sizes. In physical systems (like magnetically frustrated Josephson junction arrays and superconducting wire networks), the presence of additional interactions must lead to a better stabilization of a phase with a long-range order in terms of vortex pattern and improve the possibilities of its observation.