## 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. |

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Love the book!

Makes you want to read the whole book in one day!

It's very clear, informative and hilarious!

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To read through this book would be the nice first step to learn percolation theory, from the basic to the application. You can check the relationship between diffusion of particles and critical values in percolation theory. You can find reasonable examples of fractal structures and the relationship of them with percolation phenomena.

### 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 |

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### Common terms and phrases

Aharony approximation arguments 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 curve density derived diffusion distance diverges droplet equal Equation exact example exponential external perimeter factor ferromagnetic finite finite-size scaling fluid fractal dimension geometrical infinite cluster infinite network infinity Ising model label large clusters large lattices largest cluster lattice animals linear magnetization mass mean cluster Monte Carlo multifractal nearest neighbours ns(p occupied sites one-dimensional p>pc 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 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