An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we prove that in the scaling limit, the distribution of height is conformally invariant and converges to a Gaussian free field.
Cite this article
Zhongyang Li, Conformal invariance of dimer heights on isoradial double graphs. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 (2017), no. 3, pp. 273–307DOI 10.4171/AIHPD/41