Random Fields and Spin Glasses: A Field Theory Approach

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Overview

Disordered magnetic systems enjoy non-trivial properties which are different and richer than those observed in their pure, non-disordered counterparts. These properties dramatically affect the thermodynamic behaviour and require specific theoretical treatment. This 2006 book deals with the theory of magnetic systems in the presence of frozen disorder, in particular paradigmatic and well-known spin models such as the Random Field Ising Model and the Ising Spin Glass. This is a unified presentation using a field theory language which covers mean field theory, dynamics and perturbation expansion within the same theoretical framework. Particular emphasis is given to the connections between different approaches such as statics vs. dynamics, microscopic vs. phenomenological models. The book introduces some useful and little-known techniques in statistical mechanics and field theory. This book will be of great interest to graduate students and researchers in statistical physics and basic field theory.

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Editorial Reviews

From the Publisher
"All in all the book will take an important place on the desk of everyone working in this exciting field of research. In particular, it should be highly recommended to mathematicians and mathematical physicists who want to get thoroughly acquainted with the methods and results of theoretical physics in this field."
Anton Bovier, Mathematical Reviews

"It is written in masterly and elegant fashion by two remarkable researchers who have themselves, in particular prof. De Dominicis, fundamentally contributed to the subject. The authors masterly wield the various methods of the field theory in order to "clarify and unify" via its mathematical language some of, in their opinion, more cryptic and pointed details of the theory of disordered systems."
Rudi Podgornik for the Journal of Statistical Physics

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Product Details

  • ISBN-13: 9780521847834
  • Publisher: Cambridge University Press
  • Publication date: 11/30/2006
  • Edition description: First Edition
  • Pages: 230
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.63 (d)

Meet the Author

Cirano De Dominicis is affiliated with the Service de Physique Théoretique, Centre Commissariat ... l'Energie Atomique (CEA), Saclay, France. He has won several prizes including the Langevin prize and Ricard prize from the French Physical Society, the Ampere prize from the French Academy of Sciences, and the Silver Medal of the National Center of Scientific Research.

Irene Giardina is a researcher at the Istituto Nazionale de Fisica della Materia, Consiglio Nazionale delle Ricerche (CNR), and is also affiliated with the Department of Physics at the University of Rome La Sapienza, Italy.

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Table of Contents

1. A brief introduction; 2. The Random Field Ising model; 3. The dynamical approach; 4. The p=2 spherical model; 5. Mean field spin glasses: one-step RSB; 6. The Sherrington–Kirkpatrick model; 7. Mean field via TAP equations; 8. Spin glass above D=6; 9. Propagators, mostly replicon; 10. Ward–Takahashi identities and Goldstone modes; 11. Alternative approaches and conclusions; Appendices; Index.

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