Near-critical dimers and massive SLE

12.06.2023 16:15 – 18:15

A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane.
In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the "imaginary geometry" approach developed in earlier work with Benoit Laslier and Gourab Ray, as well as a new exact discrete Girsanov identity on the triangular lattice.
Time-permitting we will discuss conjectures relating this model to the sine-Gordon model.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre