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Seminar

AGRS Research Seminar Series: Near-Critical Dimers and Massive SLE May 18, 2022 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: The Analysis and Geometry of Random Spaces MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Nathanael Berestycki (University of Vienna)
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Video

AGRS Research Seminar Series: Near-Critical Dimers And Massive SLE

Abstract/Media

To participate in this seminar, please register HERE.

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. This near-critical model can be thought of as describing the boundary between the liquid and gaseous phases of the model.

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 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. No prerequisite on the dimer model will be assumed; the talk will be self-contained.