© 1999

Conformal Invariance and Critical Phenomena

  • Nowhere else is there such a complete account of the finite-size scaling predictions and numerical texts of the theory (J. Cardy in Physics Today).


Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Malte Henkel
    Pages 1-42
  3. Malte Henkel
    Pages 43-62
  4. Malte Henkel
    Pages 63-82
  5. Malte Henkel
    Pages 117-126
  6. Malte Henkel
    Pages 127-140
  7. Malte Henkel
    Pages 141-156
  8. Malte Henkel
    Pages 157-182
  9. Malte Henkel
    Pages 205-218
  10. Malte Henkel
    Pages 219-260
  11. Malte Henkel
    Pages 261-278
  12. Malte Henkel
    Pages 279-320
  13. Malte Henkel
    Pages 321-368
  14. Malte Henkel
    Pages 369-384
  15. Back Matter
    Pages 385-417

About this book


This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.


Application of integrable systems in statistical physics Computational Physics Critical Phenomena Infinite-dimensional Lie algebras Phase Transitions Quantum Field Theory algebra numerical methods

Authors and affiliations

  1. 1.Laboratoire de Physique des Matériaux CNRS-UMR 7556Université Henri Poincaré Nancy IVandœuvre lès NancyFrance

Bibliographic information

Industry Sectors
Energy, Utilities & Environment