Monte Carlo simulation of the three-dimensional XY model with bilinear-biquadratic exchange interaction

The three-dimensional XY model with bilinear-biquadratic exchange interacti ons J and J ', respectively, has been studied by Monte Carlo simulations. F rom the detailed analysis of the thermal variation of various physical quan tities, as well as the order parameter and energy histogram analysis, the p hase diagram including two different ordered phases has been determined. Th ere is a single phase boundary from a paramagnetic to a dipole-quadrupole o rdered phase, which is of second order in a high J/J ' ratio region, changi ng to a first-order one for 0.35 less than or equal toJ/J ' less than or eq ual to0.5. Below J/J ' = 0.35 there are two separate transitions: the first one to the quadrupole long-range order (QLRO) phase at higher temperatures , followed by another one to the dipole-quadrupole long-range order (DLRO) phase at lower temperatures. The finite-size scaling analysis yields values of the critical exponents For both the DLRO and QLRO transitions close to the values for the conventional XY model which includes no biquadratic exch ange, (C) 2001 Elsevier Science B.V. All rights reserved.