2nd Edition

Introduction To Percolation Theory Second Edition

By Dietrich Stauffer, Ammon Aharony Copyright 1992
    192 Pages
    by Taylor & Francis

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    This 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.

    Preface to the Second Edition
    Preface to the First Edition
    Introduction: Forest Fires, Fractal Oil Fields, and Diffusion
    What is percolation?
    Forest fires
    Oil fields and fractals
    Diffusion in disordered media
    Coming attractions
    Further reading
    Cluster Numbers
    The truth about percolation
    Exact solution in one dimension
    Small clusters and animals in d dimensions
    Exact solution for the Bethe lattice
    Towards a scaling solution for cluster numbers
    Scaling assumptions for cluster numbers
    Numerical tests
    Cluster numbers away from Pc
    Further reading
    Cluster Structure
    Is the cluster perimeter a real perimeter?
    Cluster radius and fractal dimension
    Another view on scaling
    The infinite cluster at the threshold
    Further reading
    Finite-size Scaling and the Renormalization Group
    Finite-size scaling
    Small cell renormalization
    Scaling revisited
    Large cell and Monte Carlo renormalization
    Connection to geometry
    Further reading
    Conductivity and Related Properties
    Conductivity of random resistor networks
    Internal structure of the infinite cluster
    Multitude of fractal dimensions on the incipient infinite cluster
    Fractal models
    Renormalization group for internal cluster structure
    Continuum percolation, Swiss-cheese models and broad distributions
    Elastic networks
    Further reading
    Walks, Dynamics and Quantum Effects
    Ants in the labyrinth
    Probability distributions
    Fractons and superlocalization
    Hulls and external accessible perimeters
    Diffusion fronts
    Invasion percolation
    Further reading
    Application to Thermal Phase Transitions
    Statistical physics and the Ising model
    Dilute magnets at low temperatures
    History of droplet descriptions for fluids
    Droplet definition for the Ising model in zero field
    The trouble with Kertesz
    Dilute magnets at finite temperatures
    Spin glasses
    Further reading
    Numerical Techniques