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 $q=3$. 
G. A. Canova and F. C. Poderoso and J. J. Arenzon and Y. Levin
cond-mat.stat-mech