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Random Fields And Spin Glasses

Author: Cirano De Dominicis
Publisher: Cambridge University Press
ISBN: 9780521847834
Size: 15.42 MB
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The book introduces some useful and little known techniques in statistical mechanics and field theory including multiple Legendre transforms, supersymmetry, Fourier transforms on a tree, infinitesimal permutations and Ward Takahashi Identities."--Jacket.

Spin Glasses And Random Fields

Author: A. Peter Young
Publisher: World Scientific
ISBN: 9810232403
Size: 71.25 MB
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The last few years have seen many developments in the study of ?frustrated? systems, such as spin glasses and random fields. In addition, the application of the idea of spin glasses to other branches of physics, such as vortex lines in high temperature superconductors, protein folding, structural glasses, and the vulcanization of rubber, has been flourishing. The earlier reviews are several years old, so now is an appropriate time to summarize the recent developments. The articles in this book have been written by leading researchers and include theoretical and experimental studies, and large-scale numerical work (using state-of-the-art algorithms designed specifically for spin-glass-type problems), as well as analytical studies.

Rugged Free Energy Landscapes

Author: Wolfhard Janke
Publisher: Springer Science & Business Media
ISBN: 3540740252
Size: 32.91 MB
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This collection of lectures and tutorial reviews by renowned experts focusses on the common computational approaches in use to unravel the static and dynamical behaviour of complex physical systems at the interface of physics, chemistry and biology. Paradigmatic examples of condensed matter physics are spin and structural glasses and protein folding, as well as their aggregation and adsorption to hard and soft surfaces, in physico-chemical biology. Among the most prominent joint key features of the systems considered in this volume are rugged free-energy landscapes. These generate metastability and are often responsible for very slow dynamics allowing for the system to be trapped in one of the many available local minima. The challenge set forth by the authors of this volume is to provide a common basis and technical language for the (computational) technology transfer between the fields and systems considered.

Statistical Physics Of Spin Glasses And Information Processing

Author: Hidetoshi Nishimori
Publisher: Clarendon Press
ISBN: 9780198509400
Size: 65.72 MB
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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

Random Walks Random Fields And Disordered Systems

Author: Anton Bovier
Publisher: Springer
ISBN: 3319193392
Size: 22.81 MB
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Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.

Spin Glasses

Author: K. H. Fischer
Publisher: Cambridge University Press
ISBN: 9780521447775
Size: 24.34 MB
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A comprehensive account of the theory, experimental work and computer modelling of spin glasses.

Spin Glasses A Challenge For Mathematicians

Author: Michel Talagrand
Publisher: Springer Science & Business Media
ISBN: 9783540003564
Size: 20.35 MB
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In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.

Quantum Monte Carlo Methods In Condensed Matter Physics

Author: Masuo Suzuki
Publisher: World Scientific
ISBN: 9789810236830
Size: 70.79 MB
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This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-c superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.

Mean Field Models For Spin Glasses

Author: Michel Talagrand
Publisher: Springer Science & Business Media
ISBN: 9783642152023
Size: 34.52 MB
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This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.