Commensurate and Incommensurate Vortices in Two-Dimensional XY Models

Simple, nearest-neighbor XY models on unfrustrated lattices with competing ferromagnetic [cos()] and nematic [cos(2)] interactions are studied. For sufficiently strong competition, this model exhibits four phases in spatial dimension d=3 and five in d=2, 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 their unbinding mediates the phase transitions, which are all of the Kosterlitz-Thouless type. © 1986 The American Physical Society.