Thursday, March 10, 2022
4:00 PM -
5:00 PM
LA Probability Forum
An elementary proof of phase transition in the planar XY model
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.
Event Sponsors:
For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].