Bratelli O. - Operator Algebras and Quantum Statistical Mechanics Vol. 2 (2nd ed.)
Preface to the Second Edition
Fifteen years have passed since completion of the first edition of this book
and much has happened. Any attempt to do justice to the new develop-
ments would necessitate at least one new volume rather than a second
edition of the current one. Fortunately other authors have taken up the
challenge of describing these discoveries and our bibliography includes
references to a variety of new books that have appeared or are about to
appear. We consequently deided to keep the format of this book as a basic
reference for the operator algebraic approach to quantum statistical me-
chanics and concentrated on correcting, improving, and updating the
material of the first edition. This in itself has not been easy and changes
occur throughout the text. The major changes are a corrected presentation
of Bose-Einstein condensation in Theorem 5.2.30, insertion of a general
result on the absence of symmetry breaking in Theorem 5.3.33A, and an
extended description of the dynamics of the X- model in Example 6.2.14.
The discussion of phase transitions in specific models, in Sects. 6.2.6 and
6.2.7, has been expanded with the focus shifted from the classical Ising
model to genuine quantum situations such as the Heisenberg and X-Y
models. In addition the Notes and Remarks to various subsections have
been considerably augmented.
Since our interest in the subject of equilibrium states and models of
statistical mechanics has waned considerably in the last fifteen years it
would have been impossible to prepare this second edition without the
support and encouragement of many of our friends and colleagues. We are
particularly indebted to Charles Batty, Michiel van den Berg, Tom ter Elst,
Dai Evans, Mark Fannes, Jfirg Fr6hlich, Taku Matsui, Andr Verbeure,
and Marinus Winnink for information and helpful advice, and we apol-
ogize for often ignoring the latter. We are especially grateful to Aernout
van Enter and Reinhard Werner for counselling us on recent developments
and giving detailed suggestions for revisions.
Oslo and Canberra 1996
Ola Bratteli
Derek W. Robinson
- Paperback: 530 pages
- Publisher: Springer (July 31, 2012)
- Language: English
- ISBN-10: 3642082572
- ISBN-13: 978-3642082573
Preface to the Second Edition
Fifteen years have passed since completion of the first edition of this book
and much has happened. Any attempt to do justice to the new develop-
ments would necessitate at least one new volume rather than a second
edition of the current one. Fortunately other authors have taken up the
challenge of describing these discoveries and our bibliography includes
references to a variety of new books that have appeared or are about to
appear. We consequently deided to keep the format of this book as a basic
reference for the operator algebraic approach to quantum statistical me-
chanics and concentrated on correcting, improving, and updating the
material of the first edition. This in itself has not been easy and changes
occur throughout the text. The major changes are a corrected presentation
of Bose-Einstein condensation in Theorem 5.2.30, insertion of a general
result on the absence of symmetry breaking in Theorem 5.3.33A, and an
extended description of the dynamics of the X- model in Example 6.2.14.
The discussion of phase transitions in specific models, in Sects. 6.2.6 and
6.2.7, has been expanded with the focus shifted from the classical Ising
model to genuine quantum situations such as the Heisenberg and X-Y
models. In addition the Notes and Remarks to various subsections have
been considerably augmented.
Since our interest in the subject of equilibrium states and models of
statistical mechanics has waned considerably in the last fifteen years it
would have been impossible to prepare this second edition without the
support and encouragement of many of our friends and colleagues. We are
particularly indebted to Charles Batty, Michiel van den Berg, Tom ter Elst,
Dai Evans, Mark Fannes, Jfirg Fr6hlich, Taku Matsui, Andr Verbeure,
and Marinus Winnink for information and helpful advice, and we apol-
ogize for often ignoring the latter. We are especially grateful to Aernout
van Enter and Reinhard Werner for counselling us on recent developments
and giving detailed suggestions for revisions.
Oslo and Canberra 1996
Ola Bratteli
Derek W. Robinson
