The lectures will follow closely the book Complexity and Criticality by Christensen
and Moloney. No other reference book is needed.
However, for completeness, please find a short list of other relevant books.
The first book listed below will cover most of the concepts related to
The following two books are introductions to phase transitions and the
concept of universality and they will basically cover everything given
in the lectures related to the Ising model.
The last two books are references on complexity and self-organised
criticality. The book by Jensen is more technical
than the book by Bak.
Authors: Dietrich Stauffer & Amnon Aharony.
Title: Introduction to Percolation Theory.
Publisher: Taylor & Francis, 1994.
ISBN: 0-74-840253-5 (paperback).
Price: About 22 pounds.
Percolation theory deals with clustering, criticality,
fractals, phase transitions and disordered systems.
It provides a quantitative model for understanding these phenomena,
and therefore provides a theoretical, statistical background to many
physical and natural science disciplines.
Readers are expected to be able to handle some fundamental
mathematical procedures such as integration and differentiation of single
variable functions, probability and statistics.
Author: Nigel Goldenfeld.
Title: Lectures on Phase Transitions and the Renormalisation Group.
Publisher: Westview Press, 1992.
Price: ?? pounds.
Covering the elementary aspects of the physics of phases transitions and the renormalisation group, this popular book is
widely used both for core graduate statistical mechanics courses as well as for more specialised courses.
Emphasising understanding and clarity rather than technical manipulation, these lectures de-mystify the subject
and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done,
what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists,
students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the
introductory graduate level. Advanced, never-before-printed topics on the applications of renormalisation group
far from equilibrium and to partial differential equations add to the uniqueness of this book.
Author: Julia M. Yeomans.
Title: Statistical Mechanisc of Phase Transitions.
Publisher: Oxford Science Publications, 1992.
ISBN: 0-19-851730-0 (paperback).
Price: About 20 pounds.
Recent developments have led to a good understanding of
universality; why phase transitions in systems as diverse as
magnets, fluids, liquid crystals, and superconductors can be
brought under the same theoretical umbrella and well
described by simple models. This work describes the physics underlying
universality and then lays out the theoretical approaches now available for
studying phase transitions.
Author: Per Bak.
Title: How Nature Works: the Science of Self-Organized Criticality.
Publisher: Springer Verlag, New York, 1996.
ISBN: ISBN 0-387-98738-X (paperback).
Price: About 15 pounds.
This book on self-organized criticality, describes for the general
reader a concept that has become increasingly important in science.
Many seemingly disparate aspects of the world, from the formation
of the landscape to the process of evolution to the action of nervous
systems to the behaviour of the economy all share a set of simple, easily
described properties. These are often described as emergent properties.
Bak argues that these properties are all so similar that they look
to be manifestations of a single principle, a Newton's Law of complex
behaviour. Further, he claims that SOC, the spontaneous development
of systems to a critical state, is the key to such a principle.
Author: Henrik J. Jensen.
Title: Self-Organized Criticality: Emergent Complex Behaviour
in Physical and Biological Systems.
Publisher: Cambridge, University Press, 1998.
ISBN: 0-521-48371-9 (paperback).
Price: About 20 pounds.
Self-organized criticality (SOC) is based upon the idea that
complex behaviour can develop spontaneously in certain multi-body
systems whose dynamics vary abruptly. This book is a concise introduction
to the field of SOC, and contains an overview of the main research results.
The author assumes no previous knowledge of the field, and the book
contains several exercises. It is intended as a
textbook for graduate students taking physics, engineering, or mathematical
biology courses in nonlinear science or complexity.