Three generalizations of the fully frustrated triangular XY model.
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The fully frustrated triangular lattice of XY spins has nearest-neighbor antiferromagnetic interactions and a locally ordered state with three spins per unit cell, at 120to one another. Using mean-field theory and a fluctuation analysis, we have studied three generalizations, as a function of a parameter , each of which reduces to the original model for =1. The investigation arose from an attempt to obtain, for the fully frustrated triangular lattice of XY spins, the same type of generalization that was obtained by Berge et al. for Villain's "odd" model of fully frustrated XY spins on the square lattice. The three generalizations are: the "row" model, which has a preferred direction and one spin per unit cell in its Hamiltonian; the "centered honeycomb" model, which has three spins per unit cell in its Hamiltonian; and the "staggered row" model, which has three spins per unit cell and a preferred direction in its Hamiltonian. The "staggered row" model is the most complex of the three, with aspects of each of the other models and an (,T) phase diagram possessing five ordered phases and two tetracritical points. Its spiral (with three spins per unit cell) SP3 and its antiferromagnetic (with six spins per unit cell) AF6 phases are much like the spiral SP and antiferromagnetic AF phases of the row model; its ferrimagnetic (FI) and AF3 phases have the same symmetry as the corresponding phases of the "centered honeycomb" model, and its noncollinear NC6 phase is related to the NC3 phase of the "centered honeycomb" model. Comparison between the models enables us to distinguish those properties that are due to three spins per unit cell from those due to the preferred direction. From the phase diagrams, we conclude that the "centered honeycomb" lattice is the sought-after generalization. An analysis of the various transitions in all three models is made, to identify Ising-like and XY-like transitions. For the "staggered row" model, a fluctuation analysis that includes phase fluctuations but not amplitude fluctuations is also performed, yielding insight into the nature of the ordered phases, and the significance of the two tetracritical points. Our analysis of the phase diagram for the "centered honeycomb" model suggests that RbFeBr3 may, at low enough temperatures, undergo a phase transition from a collinear to a canted state. 1993 The American Physical Society.
