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.

An introductory book on the statistical mechanics of disordered systems, ideal for graduates and researchers.

Publisher Description

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)

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

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.

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