Kick-off event: AI and the future of mathematics and physics - 21.10.2026
In light of recent developments, the incoming kick-off event at the Institut Henri Poincaré will take the form of a debate gathering mathematicians and theoretical physicists around the role of AI in the practice of research. More information will come soon.
The near-critical dimer model and the sine-Gordon field
byLucas Rey
Abstract:The study of critical models is of the more active areas of statistical mechanics. Regarding the dimer model, the convergence of the critical model towards the Gaussian free field was obtained around 25 years ago by Kenyon. More recently, perturbations of the critical model known as near-critical models have been considered, and some convergence results have been obtained, in particular for the Ising model. Convergence results have also been obtained for the near-critical dimer model, which did not allow to identify the limiting field, even though it was conjectured to be the sine-Gordon field. I will present a derivation of the limit using discrete massive holomorphy techniques, which expresses the limiting field as the solution of a certain Dirichlet problem associated with a massive Dirac operator. I will finally explain how to relate this field to the sine-Gordon field. This is based on an ongoing work with Nathanaël Berestycki and Scott Mason.