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

TL;DR

This paper rigorously proves and numerically confirms a phase transition between paramagnetic and nematic phases in generalized XY models, validating previous phase diagram predictions and challenging earlier heuristic arguments against the nematic phase for q=3.

Contribution

It provides the first rigorous proof and extensive simulations demonstrating the phase transition in generalized XY models, confirming the phase diagram topology.

Findings

Confirmed the existence of a paramagnetic-nematic transition

Validated the phase diagram proposed by Poderoso et al.

Disproved Korshunov's heuristic argument against the nematic phase for q=3

Abstract

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 $q=3$.