Scaling and Renormalization in Statistical Physics

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Cambridge University Press, 26.04.1996 - 238 Seiten
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This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behavior, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behavior, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.
 

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Inhalt

Phase transitions in simple systems
1
Mean field theory
16
The renormalization group idea
28
Phase diagrams and fixed points
61
The perturbative renormalization group
83
Low dimensional systems
111
Surface critical behaviour
133
Random systems
145
Polymer statistics
169
Critical dynamics
183
Conformal symmetry
206
Gaussian integration
227
Index
234
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