We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso et al. [Phys. Rev. Lett. 106, 067202 (2011)]. 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 three-states Potts universality class
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