A new approach to the Berezinskii–Kosterlitz–Thouless transition in the planar XY model
VIENNA PROBABILITY SEMINAR
Date:
Thursday, September 30, 2021 14:00 - 14:50
Speaker:
Marcin Lis (Uni Wien)
Location:
Rényi Institute Budapest
Series:
Mathematics and CS Seminar
Host:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Contact:
Birgit Oosthuizen-Noczil
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.