THE XY SPIN-GLASS IN THE PRESENCE OF A PLANAR ANISOTROPY-FIELD

We consider the infinite-range XY spin glass in the presence of a p-fo ld anisotropy parameter D-p, favouring p orientations in a plane. This model interpolates between the XY (D-p --> 0) and p-state clock (D-p --> infinity) spin glasses. For p greater than or equal to 4, D-p is i rrelevant in what concerns the qualitative behaviour of the Parisi fun ction. Special attention is devoted to the p = 3 case, for which the r eplica-symmetry-breaking scheme leads to very distinct order-parameter functions in the two end-point limits. We analyse the evolution of th e Parisi function for varying D-3 and find two distinct crossovers in its shape. We evaluate the anisotropy parameter (D3()) at the crossov er and find that the Parisi function changes from its conventional beh aviour (continuous and monotonically increasing), typical of the XY sp in glass (D-3 < D-3), to the step function characteristic of Potts sp in glasses (D-3 greater than or equal to D-3).