Bipartite dimer model: perfect tembeddings and Lorentzminimal surfaces
Abstract
This is the second paper in the series devoted to the study of the dimer model on tembeddings of planar bipartite graphs. We introduce the notion of perfect tembeddings and assume that the graphs of the associated origami maps converge to a Lorentzminimal 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.06272
 Bibcode:
 2021arXiv210906272C
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Complex Variables;
 82B20;
 30G25;
 53A10
 EPrint:
 39 pages, 3 figures