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Conformal Invariance and Critical Phenomena

  • Textbook
  • © 1999

Overview

Authors:
  1. Malte Henkel

    1. Laboratoire de Physique des Matériaux CNRS-UMR 7556, Université Henri Poincaré Nancy I, Vandœuvre lès Nancy, France

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  • 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).
  • Includes supplementary material: sn.pub/extras

Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Critical Phenomena: a Reminder

    • Malte Henkel
    Pages 1-42

  3. Conformal Invariance

    • Malte Henkel
    Pages 43-62

  4. Finite-Size Scaling

    • Malte Henkel
    Pages 63-82

  5. Representation Theory of the Virasoro Algebra

    • Malte Henkel
    Pages 83-100

  6. Correlators, Null Vectors and Operator Algebra

    • Malte Henkel
    Pages 101-116

  7. Ising Model Correlators

    • Malte Henkel
    Pages 117-126

  8. Coulomb Gas Realization

    • Malte Henkel
    Pages 127-140

  9. The Hamiltonian Limit and Universality

    • Malte Henkel
    Pages 141-156

  10. Numerical Techniques

    • Malte Henkel
    Pages 157-182

  11. Conformal Invariance in the Ising Quantum Chain

    • Malte Henkel
    Pages 183-204

  12. Modular Invariance

    • Malte Henkel
    Pages 205-218

  13. Further Developments and Applications

    • Malte Henkel
    Pages 219-260

  14. Conformal Perturbation Theory

    • Malte Henkel
    Pages 261-278

  15. The Vicinity of the Critical Point

    • Malte Henkel
    Pages 279-320

  16. Surface Critical Phenomena

    • Malte Henkel
    Pages 321-368

  17. Strongly Anisotropic Scaling

    • Malte Henkel
    Pages 369-384

  18. Back Matter

    Pages 385-417
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Keywords

About this book

Critical phenomena arise in a wide variety of physical systems. Classi­ cal examples are the liquid-vapour critical point or the paramagnetic­ ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur­ bulence and may even extend to the quark-gluon plasma and the early uni­ verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal­ ing, provided only that angles remain unchanged.

Authors and Affiliations

  • Laboratoire de Physique des Matériaux CNRS-UMR 7556, Université Henri Poincaré Nancy I, Vandœuvre lès Nancy, France

    Malte Henkel

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