Introduction to the Replica Theory of Disordered Statistical Systems
Introduction to the Replica Theory of Disordered Statistical Systems
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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.
- Comprehensive survey of statistical mechanics of disordered systems from the elementary level up to the frontiers of modern research
- The first book to give a systematic description of the theory of critical phenomena in disordered systems
- Self-contained treatment of the subject containing results from recent research
Reviews & endorsements
'… 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 MATH
Product details
October 2005Paperback
9780521021258
236 pages
245 × 170 × 13 mm
0.385kg
35 b/w illus.
Available
Table of Contents
- 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.
