Statistical Physics of Spin Glasses and Information Processing

An Introduction
Erscheinungsjahr 2001
ISBN: 978-0-19-850941-7
Verlag: OUP Oxford

Buch, Englisch, 256 Seiten, Print PDF, Format (B × H): 156 mm x 234 mm, Gewicht: 395 g

Spin glasses are magnetic materials. Statistical mechanics, a subfield of physics, has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have turned out to offer new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. This book is one of the first publications of the past ten years that provide a broad overview of this interdisciplinary field. Most of the book is written in a self-contained manner, assuming only a general knowledge of statistical mechanics and basic probability theory. It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments.

Autoren/Hrsg.

Nishimori, Hidetoshi

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Operations Research
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie

Inhaltsverzeichnis

- 1: Mean-field theory of phase transitions

- 2: Mean-field theory of spin glasses

- 3: Replica symmetry breaking

- 4: Gauge theory of spin glasses

- 5: Error-correcting codes

- 6: Image restoration

- 7: Associative memory

- 8: Learning in perceptron

- 9: Optimization problems

- A. Eigenvalues of the Hessian

- B. Parisi equation

- C. Channel coding theorem

- D. Distribution and free energy of K-Sat

- References

- Index

Über Autor(innen)

Professor Hidetoshi Nishimori, Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan, Tel.: [phone], Fax: [phone], email: [e-mail]