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We develop a new functional renormalization group (FRG) approach for thetwo-dimensional XY-model by combining the lattice FRG proposed by Machado andDupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation whichexplicitly introduces vortices via an integer-valued field. We show that thehierarchy of FRG flow equations for the infinite set of relevant and marginalcouplings of the model can be reduced to the well-known Kosterlitz-Thoulessrenormalization group equations for the renormalized temperature and the vortexfugacity. Within our approach it is straightforward to include weak amplitudeas well as out-of-plane fluctuations of the spins, which lead to additionalinteractions between the vortices that do not spoil theBerezinskii-Kosterlitz-Thouless transition. This demonstrates that previousfailures to obtain a line of true fixed points within the FRG are amathematical artifact of insufficient truncation schemes.

physical review. e

Dual lattice functional renormalization group for the  Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and  out-of-plane fluctuations