Ground state of a model with competing interactions and spin anisotropy

Recent experiments on rare-earth multilayers have led to its being important to understand in detail the phase diagrams of models with competing interactions and spin anisotropy. Therefore we study the ground state of the XY model with competing first- and second-neighbor interactions and sixfold anisotropy, D. Infinite series of long-period phases are found to be stable. Particular attention is given to the evolution between the continuous spin and the discrete spin limits as D is increased from zero to infinity.