Reply to "Incommensurate vortices and phase transitions in two-dimensional XY models with interaction having auxiliary minima" by S. E. Korshunov

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 $q=3$.