The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Softcover)

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LIKE NEW: This book is in excellent, like-new condition. It was printed on acid-free paper.

Product Details

This book is part of theOxford Science Publications collection from Oxford University Press.

From the back cover: "The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last twenty-five years. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in may areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques at a level suitable for beginning graduate students. The text assumes only a sound undergraduate background in physics and mathematics. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions, and techniques for numerical simulation. Next, the real-space renormalization group and mean-field theory are explained and illustrated. The last eight chapters cover the Landau-Ginzburg model, from physical motivations, through diagrammatic perturbation theory and renormalization, to the renormalization group and the calculation of critical exponents above and below the critical temperature."

Chapters

1. Introduction
2. Statistical mechanics
3. Models
4. Numerical simulation
5. Real-space renormalization
6. Mean-field theory
7. The Landau-Ginzburg model
8. Diagrammatic perturbation theory
9. Renormalization
10. The calculation of critical exponents for T ≥ T_c
11. The renormalization group at T ≠ T_c
12. The lower critical dimension
13. Universality

Appendices

1. The magnetic scattering of neutrons
2. The natural variables for thermodynamic potentials
3. Magnetic energy
4. Connected correlation functions and log Z[J]
5. The Gibbs free energy
6. Discrete Fourier transforms
7. The method of steepest descent
8. Counting closed loops on a square lattice
9. Einstein's fluctuation theory
10. The Gaussian transformation
11. The Landau-Ginzburg model and the Ising model
12. Functional differentiation and integration
13. The Feynman rules for the vertex functions
14. Feymann rules for generalized Landau-Ginzburg models

Each chapter has a set of problems. The textbook concludes with Answers, References, and Index.