The Z-invariant massive Laplacian on isoradial graphs

Co-authors: Béatrice de Tilière (LPMA, UPMC), Kilian Raschel (LMPT, University of Tours)

Isoradial graphs form an interesting subset of planar graphs to study critical integrable models: the geometric properties of their embedding are related to the Yang-Baxter equation and allows one to develop a discrete theory of complex analysis.

After having reviewed some results about critical models on those graphs, we will define a massive Laplacian on isoradial graphs with integrability properties.

This massive Laplacian can be used to study off-criticality models from statistical mechanics on these infinite non-periodic graphs (e.g. spanning forests), for which local correlations are obtained, and phase transition as the mass vanishes can be studied analytically.