Spin Glasses and Complexity


Book Description

This primer builds the theory of spin glasses, starting with the real physical systems and experiments that inspired the theory.




Spin Glasses and Complexity


Book Description

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.




Spin Glasses


Book Description

A comprehensive account of the theory, experimental work and computer modelling of spin glasses.




The Sherrington-Kirkpatrick Model


Book Description

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.




Spin Glasses And Biology


Book Description

This volume is an introduction to the application of techniques developed for the study of disordered systems to problems which arise in biology. Topics presented include neural networks, adaptation and evolution, maturation of the immune response, and protein dynamics and folding. This book will appeal to students and researchers interested in statistical and condensed matter physics, glasses and spin glasses, and biophysics.




Statistical Physics of Spin Glasses and Information Processing


Book Description

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




Information, Physics, and Computation


Book Description

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.




Spin Glass Theory And Beyond: An Introduction To The Replica Method And Its Applications


Book Description

This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.




Theory of Simple Glasses


Book Description

This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.