LA Probability Forum

Will be held at UCLA - talks in Math Sciences Room 6627

We derive, with elementary methods, a power-law bound on the two-point function of the planar XY model at low temperatures and therefore show the model undergoes a Berezinskii-Kosterlitz-Thouless phase transition. This was famously first rigorously proved by Fröhlich and Spencer in the eighties. Our argument relies on a new loop representation of spin correlations and a recent result by Lammers on the delocalisation of integer-valued height functions. The main contribution is a switching lemma for the loop representation that can also be used to prove some classical correlation inequalities. Joint work with Marcin Lis.