Scaling and Renormalization in Statistical Physics
This book provides an introduction to the concepts which underlie the
modern understanding of the behaviour of complicated physical systems
which exhibit the property of scale invariance or self-similarity.
This is most clearly illustrated in materials, such as magnets or
fluids, in the vicinity of a second order phase transition.
The theoretical framework for understanding these phenomena, known as
the renormalization group, first arose in the late 1960s
and has evolved into a
common language used by workers in such diverse fields as
particle physics, cosmology, neural networks and biophysics, as well as
the more conventional aspects of condensed matter physics.
Beginning with a brief review of phase transitions in simple systems and
of mean field theory, the text then goes on to introduce the core ideas of
the renormalization group. Following chapters cover phase diagrams, fixed
points, cross-over behaviour, finite-size scaling, perturbative
renormalization methods, low-dimensional systems, surface critical
behaviour, random systems, percolation, polymer statistics, critical
dynamics and conformal symmetry. The book closes with an appendix on
Gaussian integration, a selected bibliography, and a detailed index.
Many problems are included.
The emphasis throughout is on providing an elementary and intuitive
approach. In particular, the perturbative method introduced leads, among
other applications, to a simple derivation of the epsilon expansion in
which all the actual calculations (at least to lowest order) reduce to
simple counting, avoiding the need for Feynman diagrams.