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

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arxiv 2109.06272 v1 pith:IUPBW74H submitted 2021-09-13 math.PR math-phmath.CVmath.MP

Dmitry Chelkak , Benoît Laslier , Marianna Russkikh This is my paper · ORCID
classification math.PRmath-phmath.CVmath.MP
keywords t-embeddingsbipartiteconvergedimergraphslorentz-minimalmathrmmodel
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abstract

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.

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Cited by 4 Pith papers

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  4. Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond

    math-ph 2025-08 unverdicted novelty 6.0 of 10

    The t-embedding and origami-map positions of the two-periodic Aztec diamond equal sums of octahedron-equation density functions with flat initial conditions.

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