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Artificial neural networks, learning, statistical mechanics; background material in mathematics and physics; examples and exercises; textbook/reference.
Statistical Mechanics is an integral part of theoretical physics, and this book aims at presenting the fundamentals of statistical mechanics in a clear and concise manner. The book begins with a clear exposition of classical as well as quantal equilibrium statistical mechanics. Then it moves on to give insights into the Gibbs canonical distribution, the grand canonical distribution, ideal Bose gas, ideal fermi gas, and imperfect gases. The text also delves into certain topics of special interest, such as phase-transitions, Ising model, and liquid Helium. The book concludes with a discussion of some selected topics of non-equilibrium statistical mechanics. Primarily intended as a text for postgraduate students of physics, it would also prove useful for students at the undergraduate level.
The book provides an introduction to the physics which underlies phase transitions and to the theoretical techniques currently at our disposal for understanding them. It will be useful for advanced undergraduates, for post-graduate students undertaking research in related fields, and for established researchers in experimental physics, chemistry, and metallurgy as an exposition of current theoretical understanding. - ;Recent developments have led to a good understanding of universality; why phase transitions in systems as diverse as magnets, fluids, liquid crystals, and superconductors can be brought under the same theoretical umbrella and well described by simple models. This book describes the physics underlying universality and then lays out the theoretical approaches now available for studying phase transitions. Traditional techniques, mean-field theory, series expansions, and the transfer matrix, are described; the Monte Carlo method is covered, and two chapters are devoted to the renormalization group, which led to a break-through in the field. The book will be useful as a textbook for a course in `Phase Transitions', as an introduction for graduate students undertaking research in related fields, and as an overview for scientists in other disciplines who work with phase transitions but who are not aware of the current tools in the armoury of the theoretical physicist. - ;Introduction; Statistical mechanics and thermodynamics; Models; Mean-field theories; The transfer matrix; Series expansions; Monte Carlo simulations; The renormalization group; Implementations of the renormalization group. -
Combined for researchers and graduate students the articles from the Sitges Summer School together form an excellent survey of the applications of neural-network theory to statistical mechanics and computer-science biophysics. Various mathematical models are presented together with their interpretation, especially those to do with collective behaviour, learning and storage capacity, and dynamical stability.
In this book, 16 experts describe the application of methods of statistical physics to various areas in physics and beyond, such as financial markets, game theory, evolution and traffic planning, in which statistical physics has recently become significant.

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