Introduction To Percolation Theory: Second Edition, 2nd Edition (Paperback) book cover

Introduction To Percolation Theory

Second Edition, 2nd Edition

By Dietrich Stauffer, Ammon Aharony

Taylor & Francis

192 pages

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Paperback: 9780748402533
pub: 1994-07-18
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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.

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Organic