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Percolation et Modèle d'Ising
Wendelin Werner, Université Paris Sud, Orsay, France
A publication of the Société Mathématique de France.
cover
Cours Spécialisés--Collection SMF
2009; 161 pp; hardcover
Number: 16
ISBN-10: 2-85629-276-3
ISBN-13: 978-2-85629-276-1
List Price: US$60
Member Price: US$48
Order Code: COSP/16
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These lecture notes provide a mathematical introduction to the study of random lattice-based models from statistical physics. Through the study of percolation and of the Ising model, the author introduces the notion of phase transitions and describes some classical techniques. One of the main goals of these notes is also to present recent results of Stanislav Smirnov concerning the conformal invariance of these models in two-dimensional space.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in probability.

Table of Contents

  • Introduction
Partie I. Percolation
  • Unicité de la composante connexe infinie
  • Inégalités de corrélation
  • Décroissance exponentielle
Partie II. Percolation critique sur le réseau triangulaire
  • La théorie de Russo-Seymour-Welsh
  • La formule de Cardy-Smirnov
  • Quelques exercices sur la percolation
Partie III. FK-percolation et modèle d'lsing
  • FK-percolation sur des graphes finis
  • FK-percolation en volume infini
  • Bref retour sur Ising et Potts
Partie IV. FX-percolation et modèle d'Ising sur le réseau carré
  • FK-percolation sur le réseau carré
  • Invariance conforme du modèle d'Ising
  • Quelques exercices sur la FK-percolation
  • Commentaires bibliographiques
  • Bibliographie
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