Most of the interesting and difficult problems in statistical mechanics
arise when the constituent particles of the system interact with each
other with pair or multi particle energies. The types of behaviour which
occur in systems because of these interactions are referred to as
cooperative phenomena giving rise in many cases to phase transitions.
This book and its companion volume (Lavis and Bell 1999, referred to in
the text simply as Volume 2) are princi- pally concerned with phase
transitions in lattice systems. Due mainly to the insights gained from
scaling theory and renormalization group methods, this 1 subject has
developed very rapidly over the last thirty years. In our choice of
topics we have tried to present a good range of fundamental theory and
of applications, some of which reflect our own interests. A broad
division of material can be made between exact results and ap-
proximation methods. We have found it appropriate to include some of our
discussion of exact results in this volume and some in Volume 2. The
other main area of discussion in this volume is mean-field theory
leading to closed- form approximations. Although this is known not to
give reliable results close to a critical region, it often provides a
good qualitative picture for phase dia- grams as a whole. For
complicated systems some kind of mean-field method is often the only
tractable method available.