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This two-volume work provides a comprehensive study of the
statistical mechanics of lattice models. It introduces readers to
the main topics and the theory of phase transitions, building on a
firm mathematical and physical basis. Volume 1 contains an account
of mean-field and cluster variation methods successfully used in
many applications in solid-state physics and theoretical chemistry,
as well as an account of exact results for the Ising and six-vertex
models and those derivable by transformation methods.
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 multipartiele 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 1) are princi pally concerned with phase transitions in
lattice systems. Due mainly to the insights gained from scaling
theory and renormalization group methods, this 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
inelude some of our discussion of exact results in this volume and
some in Volume 1. Apart from this much of the discussion in Volume
1 is concerned with mean-field theory. Although this is known not
to give reliable results elose to a critical region, it often
provides a good qualitative picture for phase diagrams as a whole.
For complicated systems some kind of mean-field method is often the
only tractable method available. In this volume our main concern is
with scaling theory, algebraic methods and the renormalization
group."
This two-volume work provides a comprehensive study of the
statistical mechanics of lattice models. It introduces readers to
the main topics and the theory of phase transitions, building on a
firm mathematical and physical basis. Volume 1 contains an account
of mean-field and cluster variation methods successfully used in
many applications in solid-state physics and theoretical chemistry,
as well as an account of exact results for the Ising and six-vertex
models and those derivable by transformation methods.
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 multipartiele 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 1) are princi pally concerned with phase transitions in
lattice systems. Due mainly to the insights gained from scaling
theory and renormalization group methods, this 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
inelude some of our discussion of exact results in this volume and
some in Volume 1. Apart from this much of the discussion in Volume
1 is concerned with mean-field theory. Although this is known not
to give reliable results elose to a critical region, it often
provides a good qualitative picture for phase diagrams as a whole.
For complicated systems some kind of mean-field method is often the
only tractable method available. In this volume our main concern is
with scaling theory, algebraic methods and the renormalization
group."
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