包邮复杂性和临界状态(英文影印版)

Preface
1. Percolation
1.1 Introduction
1.2 Percolation in d=1
1.3 Percolation on the Bethe Lattice
1.4 Percolation in d=2
1.5 Cluster Number Density- Scaling Ansatz
1.6 Scaling Relations
1.7 Geometric Properties of Clusters
1.8 Finite-Size Scaling
1.9 Non-Universal Critical Occupation Probabilities
1.10 Universal Critical Exponents
1.11 Real-Space Renormalisation
1.12 Summary
Exercises
2. Ising Model
2.1 Introduction
2.2 System of Non-Interacting Spins
2.3 Quantities of Interest
2.4 Ising Model in d = 1
2.5 Mean-Field Theory of the Ising Model
2.6 Landau Theory of the Ising Model
2.7 Landau Theory of Continuous Phase Transitions
2.8 Ising Model in d = 2
2.9 Widom Scaling Ansatz
2.10 Scaling Relations
2.11Widom Scaling Form and Critical Exponents in d = 1
2.12 Non-Universal Critical Temperatures
2.13 Universal Critical Exponents
2.14 Ginzburg Criterion
2.15 Real-Space Renormalisation
2.16 Wilson's Renormalisation Group Theory
2.17 Summary
Exercises
3. Self-Organised Criticality
3.1 Introduction
3.2 BTW Model in d = 1
3.3 Mean-Field Theory of the BTW Model
3.4 Branching Process
3.5 Avalanche-Size Probability- Scaling Ansatz
3.6 Scaling Relations
3.7 Moment Analysis of Avalanche-Size Probability
3.8 BTW Model in d = 2
3.9 Ricepile Experiment and the Oslo Model
3.10 Earthquakes and the OFC Model
3.11 Rainfall
3.12 Summary
Exercises
Appendix A Taylor Expansion
Appendix B Hyperbolic Functions
Appendix C Homogeneous and Scaling Functions
Appendix D Fractals
Appendix E Data Binning
Appendix F Boltzmann Distribution
Appendix G Free Energy
Appendix H Metropolis Algorithm
Bibliography
List of Symbols
Index