OPTIMIZED MEAN-FIELD THEORY FOR THE 3-DIMENSIONAL XY SPIN MODEL

Many physical systems of interest can be mapped into the planar rotato r and XY magnetic models. We show here that the very simple approach k nown as the Onsager reaction field when applied to different arrangeme nts (sc, bcc, and fee) for the three-dimensional planar rotator model predicts values for the transition temperature which compare quantitat ively well to values obtained by more sophisticated. theories. For the XY model, we propose a renormalization of the exchange parameter so t hat the fluctuations of the out-of-plane spin component are taken into account: the results are compared to high-temperature series expansio n data.