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Introduction to Conformal Invariance and Its Applications to Critical Phenomena

  • Book
  • © 1993

Overview

Authors:
  1. P. Christe

    1. Institute for Theoretical Physics, University of Berne, Berne, Switzerland

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    You can also search for this author in PubMed   Google Scholar

  2. M. Henkel

    1. Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 16)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
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  2. Critical Phenomena: a Reminder

    Pages 1-23

  3. Conformal Invariance and the Stress-Energy Tensor

    Pages 24-37

  4. Finite Size Scaling

    Pages 38-50

  5. Representation Theory of the Virasoro Algebra

    Pages 51-64

  6. Operator Algebra and Correlation Functions

    Pages 65-75

  7. The Ising Model Correlation Functions

    Pages 76-83

  8. Coulomb Gas Realization

    Pages 84-93

  9. The Hamiltonian Limit and Universality

    Pages 94-106

  10. Numerical Techniques

    Pages 107-121

  11. Conformal Invariance in the Ising Quantum Chain

    Pages 122-136

  12. Modular Invariance

    Pages 137-147

  13. Further Developments and Applications

    Pages 148-170

  14. Conformal Perturbation Theory

    Pages 171-186

  15. The Vicinity of the Critical Point

    Pages 187-216

  16. Surface Critical Phenomena

    Pages 217-241

  17. Outlook: Beyond the Conformal Group

    Pages 242-246

  18. Back Matter

    Pages 247-260
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Keywords

About this book

The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are 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 today emphasized.

Authors and Affiliations

  • Institute for Theoretical Physics, University of Berne, Berne, Switzerland

    P. Christe

  • Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

    M. Henkel

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