Ebook: Real-Space Renormalization
- Tags: Thermodynamics, Statistical Physics Dynamical Systems and Complexity
- Series: Topics in Current Physics 30
- Year: 1982
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
The renormalization-group approach is largely responsible for the considerable success which has been achieved in the last ten years in developing a complete quantitative theory of phase transitions. Before, there was a useful physical picture of phase transitions, but a general method for making accurate quantitative predictions was lacking. Existent theories, such as the mean-field theory of Landau, sometimes reproduce phase diagrams reliably but were known to fail qualitatively near critical points, where the critical behavior is particularly interesting be cause of its universal character. In the mid 1960's Widom found that the singularities in thermodynamic quanti ties were well described by homogeneous functions. Kadanoff extended the homogeneity hypothesis to correlation functions and linked it to the idea of scale invariance. In the early 1970's Wilson showed how Kadanoff's rescaling could be explicitly carried out near the fixed point of a flow in Hamiltonian space. He made the first practical renormalization-group calculation of the flow induced by the elimination of short-wave-length Fourier components of the order-parameter field. The univer sality of the critical behavior emerges in a natural way in this approach, with a different fixed point for each universality class. The discovery by Wilson and Fisher of a systematic expansion procedure in E for a system in d = 4 - E dimen sions was followed by a cascade of calculations of critical quantities as a function of d and of the order-parameter dimensionality n.
Content:
Front Matter....Pages I-XIII
Progress and Problems in Real-Space Renormalization....Pages 1-31
Bond-Moving and Variational Methods in Real-Space Renormalization....Pages 33-56
Monte Carlo Renormalization....Pages 57-86
The Real Space Dynamic Renormalization Group....Pages 87-117
Renormalization for Quantum Systems....Pages 119-147
Application of the Real-Space Renormalization to Adsorbed Systems....Pages 149-168
Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels....Pages 169-206
Back Matter....Pages 207-216
Content:
Front Matter....Pages I-XIII
Progress and Problems in Real-Space Renormalization....Pages 1-31
Bond-Moving and Variational Methods in Real-Space Renormalization....Pages 33-56
Monte Carlo Renormalization....Pages 57-86
The Real Space Dynamic Renormalization Group....Pages 87-117
Renormalization for Quantum Systems....Pages 119-147
Application of the Real-Space Renormalization to Adsorbed Systems....Pages 149-168
Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels....Pages 169-206
Back Matter....Pages 207-216
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