  Through Quantum Monte Carlo simulation, we study the biquadratic-interaction
model with the SU(2) symmetry in two and three dimensions. The zero-temperature
phase diagrams for the two cases are identical and exhibit an intermediate
phase characterized by finite quadrupole moment, in agreement with mean-field
type arguments and the semi-classical theory. In three dimensions, we
demonstrate that the model in the quadrupolar regime has a phase transition at
a finite temperature. In contrast to predictions by mean-field theories, the
phase transition to the quadrupolar phase turns out to be of the second order.
We also examine the critical behavior in the two marginal cases with the SU(3)
symmetry.
