Quadrupolar order in isotropic Heisenberg models with biquadratic interaction

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 semiclassical 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 second order. We also examine the critical behavior in the two marginal cases with the SU(3) symmetry.