Orientational phase transitions in quantum spin systems with two-component order parameter

Renormalization-group methods are used to calculate the critical exponents for the orientational phase transition induced by an external field in a system with $XY$ symmetry at zero temperature. It is shown that in a space of arbitrary dimension the values of the exponents $\nu$ and $\eta$ remain the same as in Landau's theory $(\nu=1/2,\eta=0)$.