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

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