  We study the phase diagram and the quantum phase transitions of a
site-diluted two-dimensional O(3) quantum rotor model by means of large-scale
Monte-Carlo simulations. This system has two quantum phase transitions, a
generic one for small dilutions, and a percolation transition across the
lattice percolation threshold. We determine the critical behavior for both
transitions and for the multicritical point that separates them. In contrast to
the exotic scaling scenarios found in other random quantum systems, all these
transitions are characterized by finite-disorder fixed points with power-law
scaling. We relate our findings to a recent classification of phase transitions
with quenched disorder according to the rare region dimensionality, and we
discuss experiments in disordered quantum magnets.
