Introduction to the Replica Theory of Disordered Statistical Systems

ISBN-13: 9780521773409 / Angielski / Twarda / 2000 / 234 str.

V. Dotsenko

Opis

This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. 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. In the third part Dotsenko describes other types of disordered systems, relating them 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.

Recenzje

'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

Spis treści

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.