Introduction to the Replica Theory of Disordered Statistical Systems

Introduction to the Replica Theory of Disordered Statistical Systems
Author: Viktor Dotsenko
Publisher: Cambridge University Press
Total Pages: 236
Release: 2005-10-13
Genre: Science
ISBN: 9780521021258

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.

Mathematical Statistical Physics

Mathematical Statistical Physics
Author:
Publisher: Elsevier
Total Pages: 849
Release: 2006-06-27
Genre: Science
ISBN: 0080479235

The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians. - Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science - Roadmap to the next decade of mathematical statistical mechanics - Volume for reference years to come

Statistical Physics of Spin Glasses and Information Processing

Statistical Physics of Spin Glasses and Information Processing
Author: Hidetoshi Nishimori
Publisher: Clarendon Press
Total Pages: 264
Release: 2001
Genre: Computers
ISBN: 9780198509400

This superb new book is one of the first publications in recent years to 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 probabilty theory . It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments

An Introduction to the Theory of Spin Glasses and Neural Networks

An Introduction to the Theory of Spin Glasses and Neural Networks
Author: Viktor Dotsenko
Publisher: World Scientific
Total Pages: 172
Release: 1994
Genre: Science
ISBN: 9789810218737

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.

Statistical Physics, Optimization, Inference, and Message-Passing Algorithms

Statistical Physics, Optimization, Inference, and Message-Passing Algorithms
Author: Florent Krzakala
Publisher: Oxford University Press
Total Pages: 319
Release: 2016
Genre: Computers
ISBN: 0198743734

In the last decade, there have been an increasing convergence of interest and methods between theoretical physics and fields as diverse as probability, machine learning, optimization and compressed sensing. In particular, many theoretical and applied works in statistical physics and computer science have relied on the use of message passing algorithms and their connection to statistical physics of spin glasses. The aim of this book, especially adapted to PhD students, post-docs, and young researchers, is to present the background necessary for entering this fast developing field.

Statistical Physics of Spin Glasses and Information Processing

Statistical Physics of Spin Glasses and Information Processing
Author: Hidetoshi Nishimori
Publisher: Clarendon Press
Total Pages: 260
Release: 2001
Genre: Science
ISBN: 9780198509417

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, thesetechniques 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 abroad 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 tofollow its most recent developments.

Statistical Mechanics in a Nutshell, Second Edition

Statistical Mechanics in a Nutshell, Second Edition
Author: Luca Peliti
Publisher: Princeton University Press
Total Pages: 577
Release: 2024-08-06
Genre: Science
ISBN: 0691248451

The essential introduction to modern statistical mechanics—now completely updated and expanded Statistical mechanics is one of the most exciting areas of physics today and has applications to subjects ranging from economics and social behavior to algorithmic theory and evolutionary biology. Statistical Mechanics in a Nutshell provides a self-contained introduction to this rapidly developing field. Starting with the basics of kinetic theory and requiring only a background in elementary calculus and mechanics, this concise book discusses the most important developments of recent decades and guides readers to the very threshold of today’s cutting-edge research. Features a new chapter on stochastic thermodynamics with an introduction to the thermodynamics of information—the first treatment of its kind in an introductory textbook Offers a more detailed account of numerical simulations, including simulated annealing and other accelerated Monte Carlo methods The chapter on complex systems now features an accessible introduction to the replica theory of spin glasses and the Hopfield theory of neural networks, with an emphasis on applications Provides a new discussion of defect-mediated transitions and their implications for two-dimensional melting An invaluable resource for graduate students and advanced undergraduates seeking a compact primer on the core ideas of statistical mechanics Solutions manual (available only to instructors)

Order, Disorder And Criticality: Advanced Problems Of Phase Transition Theory - Volume 6

Order, Disorder And Criticality: Advanced Problems Of Phase Transition Theory - Volume 6
Author: Yurij Holovatch
Publisher: World Scientific
Total Pages: 294
Release: 2020-06-22
Genre: Science
ISBN: 9811216231

This book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six chapters discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As for the previous volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' — a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the topic.The level of presentation makes the book readable both for professionals and the students in the field. On a larger scale, the book may contribute to promoting and deepening studies of phase transitions and critical phenomena.