Commensurate and Incommensurate Vortices in Two-DimensionalXYModels

Simple, nearest-neighbor $\mathrm{XY}$ models on unfrustrated lattices with competing ferromagnetic $\left[cos\right(\delta \theta \left)\right]$ and nematic $\left[cos\right(2\mathrm{}\delta \theta \left)\right]$ interactions are studied. For sufficiently strong competition, this model exhibits four phases in spatial dimension $d=3\mathrm{}$ and five in $d=2\mathrm{}$, including in both cases a new phase with extensive zero-point entropy. As a result of this zero-point entropy the system does not acquire perfect order even in the zero-temperature limit. The model has vortices of both irrational and integer winding number; in $d=2\mathrm{}$ their unbinding mediates the phase transitions, which are all of the Kosterlitz-Thouless type.