World Scientific Lecture Notes in Physics - Vol. 54
AN INTRODUCTION TO THE THEORY OF SPIN GLASSES AND NEURAL NETWORKS
by V Dotsenko (Landau Inst. for Theoretical Phys.)
This book aims to describe in simple terms the new area of statistical mechanics known as spin-glasses, encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Next, the 'magic' of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be studied in the laboratory. The final chapters of the book are devoted to statistical models of neural networks.
The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.
Contents:
- The Ising Magnetic Systems
- Physics of the Spin Glass State
-
Replica Method
- Replica Symmetry Breaking
- Physics of Replica Symmetry Breaking
- Replica Symmetry Breaking Solution Near Tc
- Ultrametricity
- Scaling in the Space of Spin Glass States
- Experiments
- Partial Annealing
- Statistical Models of Neural Networks
- The Hopfield Model
- Partial Annealing in Neural Networks
- Other Kinds of Neural Networks
- Appendix: Stability of the Replica-Symmetric Solutions
Readership: Researchers and graduate students in statistical mechanics
and neural networks.
"The book by Viktor Dotsenko in large parts presents the most important results of this research based on the replica method. Although these results have been presented systematically already elsewhere (for instance in the well-known book by Amit) their concise presentation makes the book self-contained and a good introduction to the theoretical tools."
R Der
Mathematics Abstracts |
| 164pp |
Pub. date: Jan 1995 |
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