Statistical mechanics on isoradial graphs

Abstract : 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.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00546224
Contributeur : Cédric Boutillier <>
Soumis le : mardi 14 décembre 2010 - 00:56:53
Dernière modification le : mercredi 12 octobre 2016 - 01:03:40
Document(s) archivé(s) le : mardi 15 mars 2011 - 02:43:57

Fichiers

survey2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00546224, version 1
  • ARXIV : 1012.2955

Collections

UPMC | PMA | INSMI | USPC

Citation

Cédric Boutillier, Béatrice De Tilière. Statistical mechanics on isoradial graphs. 22 pages. 2010. <hal-00546224>

Partager

Métriques

Consultations de
la notice

152

Téléchargements du document

158