Lucas Rey - The near-critical dimer model and the sine-Gordon field
Автор: Seed Seminar
Загружено: 2025-12-14
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Описание:
The recording 2 from the third hybrid event for trimester on *Random forests and fermionic field theories*, held on December 10, 2025
Speaker: Lucas Rey (CEREMADE, Université Paris-Dauphine et DMA, École normale supérieure, France)
Title: The near-critical dimer model and the sine-Gordon field
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 nearcritical 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.
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