  We present a rigorous proof and extensive numerical simulations showing the
existence of a transition between the paramagnetic and nematic phases, in a
class of generalized XY models. This confirms the topology of the phase diagram
calculated by Poderoso et al. [PRL 106(2011)067202]. The results disprove the
heuristic argument presented by Korshunov in arXiv:1207.2349v1, against the
existence of the generalized-nematic phase in a model with $q=3$.
