Introduction to the Replica Theory of Disordered Statistical Systems
Published on 2. November 2000
Book
Hardback
234 pages
978-0-521-77340-9 (ISBN)
Description
This book describes the statistical mechanics of classical spin systems with quenched disorder. The first part of the book covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The technique of replica symmetry breaking is explained in detail, along with a discussion of the underlying physics. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory, which is then used to obtain a new 'random' critical regime in disordered vector ferromagnets and in the two-dimensional Ising model. The third part of the book describes other types of disordered systems, relating to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.
Reviews / Votes
'... principal strength is that it provides a clear introduction to the mathematical machinery of RSB, accessible to an advanced graduate student interested in working in the statistical mechanics of disordered systems. For this reason alone it should be part of the library of any theorist working in these areas ... Dotsenko's book will remain an important contribution.' Daniel L. Stein, Physics Today 'The breadth of the exposition, and in particular the fact that also non-mean field systems are covered, is the main merit of this text and illustrates the wide range of applicability of this method ... the book will be a useful reference for the researcher and a reasonable first introduction to the field for graduate students entering the field.' A. Bovier, Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
35 Line drawings, unspecified
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 17 mm
Weight
590 gr
ISBN-13
978-0-521-77340-9 (9780521773409)
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Schweitzer Classification
Other editions
Additional editions
Book
10/2005
Cambridge University Press
€74.30
Shipment within 15-20 days
Content
Preface; 1. Introduction; Part I. Spin-Glass Systems: 2. Physics of the spin glass state; 2. The mean-field theory of spin glasses; 4. Physics of replica symmetry breaking; 5. Ultrametricity; 6. Experiments; Part II. Critical Phenomena and Quenched Disorder: 7. Scaling theory of the critical phenomena; 8. Critical behaviour in systems with disorder; 9. Spin glass effects in the critical phenomena; 10. Two dimensional Ising model with disorder; Part III. Other Types of Disordered Systems: 11. Ising systems with quenched random fields; 12. One dimensional directed polymers in random potentials; 13. Vector breaking of replica symmetry; 14. Conclusions; References.