  As an example of ordering due to quantum fluctuations, we examine the
nearest-neighbor antiferromagnetic quantum O(n) rotor model on the pyrochlore
lattice. Classically, this system remains disordered even at zero temperature;
we find that adding quantum fluctuations induces an ordered phase that survives
to positive temperature, and we determine how its phase diagram scales with the
coupling constant and the number of spin components. We demonstrate, using
quantum Monte Carlo simulations, that this phase has long-range spin-nematic
order, and that the phase transition into it appears to be first order.
