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Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2022

Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces

Résumé

This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assume that the graphs of the associated origami maps converge to a Lorentz-minimal surface $\mathrm{S}_\xi$ as $\delta\to 0$. In this setup we prove (under very mild technical assumptions) that the gradients of the height correlation functions converge to those of the Gaussian Free Field defined in the intrinsic metric of the surface $\mathrm{S}_\xi$. We also formulate several open questions motivated by our work.

Dates et versions

hal-03733932 , version 1 (21-07-2022)

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Dmitry Chelkak, Benoît Laslier, Marianna Russkikh. Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces. Proceedings of the London Mathematical Society, In press. ⟨hal-03733932⟩
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