Introduction To Percolation TheoryThis work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups. |
Contents
Forest Fires Fractal Oil Fields and Diffusion | 1 |
Chapter 2 Cluster Numbers | 15 |
Chapter 3 Cluster Structure | 60 |
Chapter 4 FiniteSize Scaling and the Renormalization Group | 74 |
Chapter 5 Conductivity and Related Properties | 93 |
Chapter 6 Walks Dynamics and Quantum Effects | 122 |
Chapter 7 Application to Thermal Phase Transitions | 147 |
Common terms and phrases
Aharony approximation asymptotic average number backbone behaviour Bethe lattice blobs bond percolation calculate called cell Chapter cluster numbers cluster size distribution concentration conductivity configurations correlation length critical exponents critical point Curie point density derived diffusion distance diverges droplet Equation exact example exponential external perimeter factor ferromagnetic finite fluid fractal dimension geometrical infinite cluster infinite network infinity Ising model label large clusters largest cluster lattice animals linear magnetization mass mean cluster Monte Carlo multifractal nearest neighbours occupied sites one-dimensional particles percolation clusters percolation theory percolation threshold phase transitions Phys plot polymer power law probability proportional radius random numbers randomly ratio renormalization group result scaling function Section self-avoiding walks shows simple cubic lattice simulations singly connected bonds site percolation smaller spins square lattice super-site temperature thermal phase transitions three dimensions trees triangular lattice unity valid zero