A new approach to the Berezinskii–Kosterlitz–Thouless transition in the planar XY model

VIENNA PROBABILITY SEMINAR

We present a new proof of the BKT phase transition in the spin XY (planar rotor) model on any planar lattice — a result first established by Fröhlich and Spencer in 1981. Our approach is quite elementary. It does not go through the analysis of vortices but rather through the dual integer-valued height function. We use a recent result of Lammers on delcoalization of general height functions together with a new loop representation of spin correlations in the XY model, that we believe to be of independent interest. This is joint work with Diederik van Engelenburg.