  The three-dimensional XY model with bilinear-biquadratic exchange
interactions $J$ and $J'$, respectively, has been studied by Monte Carlo
simulations. From the detailed analysis of the thermal variation of various
physical quantities, as well as the order parameter and energy histogram
analysis, the phase diagram including two different ordered phases has been
determined. There is a single phase boundary from a paramagnetic to a
dipole-quadrupole ordered phase, which is of second order in a high $J/J'$
ratio region, changing to a first-order one for $0.35 \leq J/J' \leq 0.5$.
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 exchange.
