  We present extensive numerical simulations of a generalized XY model with
nematic-like terms recently proposed by Poderoso {\it et al} [PRL
106(2011)067202]. Using finite size scaling and focusing on the $q=3$ case, we
locate the transitions between the paramagnetic (P), the nematic-like (N) and
the ferromagnetic (F) phases. The results are compared with the recently
derived lower bounds for the P-N and P-F transitions. While the P-N transition
is found to be very close to the lower bound, the P-F transition occurs
significantly above the bound. Finally, the transition between the nematic-like
and the ferromagnetic phases is found to belong to the 3-states Potts
universality class.
