Introduction to Conformal Invariance and Its Applications to Critical Phenomena / by Philippe Christe, Malte Henkel.

Format:

Book

Author/Creator:

Christe, P. (Philippe), 1958- author.

Henkel, M. (Malte), 1960- author.

Series:

Lecture Notes in Physics Monographs ; 16

Language:

English

Subjects (All):

Thermodynamics.

System theory.

Mathematical physics.

Condensed matter.

Complex Systems.

Mathematical Methods in Physics.

Theoretical, Mathematical and Computational Physics.

Phase Transitions and Multiphase Systems.

Local Subjects:

Thermodynamics.

Complex Systems.

Mathematical Methods in Physics.

Theoretical, Mathematical and Computational Physics.

Phase Transitions and Multiphase Systems.

Physical Description:

1 online resource (XV, 260 p. 4 illus.)

Edition:

1st ed. 1993.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.

Summary:

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.

Contents:

Critical Phenomena: a Reminder

Conformal Invariance and the Stress-Energy Tensor

Finite Size Scaling

Representation Theory of the Virasoro Algebra

Operator Algebra and Correlation Functions

The Ising Model Correlation Functions

Coulomb Gas Realization

The Hamiltonian Limit and Universality

Numerical Techniques

Conformal Invariance in the Ising Quantum Chain

Modular Invariance

Further Developments and Applications

Conformal Perturbation Theory

The Vicinity of the Critical Point

Surface Critical Phenomena

Outlook: Beyond the Conformal Group.

Notes:

Includes bibliographical references and index.

ISBN:

3-540-47575-3