Statistical mechanics on isoradial graphs - Archive ouverte HAL Access content directly
Book Sections Year : 2012

Statistical mechanics on isoradial graphs


Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natural setting for discrete complex analysis, to which we dedicate one section. Then, we give an overview of explicit results obtained for different models of statistical mechanics defined on such graphs: the critical dimer model when the underlying graph is bipartite, the 2-dimensional critical Ising model, random walk and spanning trees and the q-state Potts model.
Fichier principal
Vignette du fichier
survey2.pdf (167.72 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00546224 , version 1 (14-12-2010)



Cédric Boutillier, Béatrice de Tilière. Statistical mechanics on isoradial graphs. Jean-Dominique Deuschel, Barbara Gentz, Wolfgang König, Max von Renesse, Michael Scheutzow, Uwe Schmock. Probability in Complex Physical Systems, 11, Springer, pp.491-512, 2012, Springer Proceedings in Mathematics, ⟨10.1007/978-3-642-23811-6_20⟩. ⟨hal-00546224⟩
149 View
483 Download



Gmail Mastodon Facebook X LinkedIn More