The Sherrington Kirkpatrick Model

Author : Dmitry Panchenko
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 48,7 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9781461462897

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The Sherrington-Kirkpatrick Model by Dmitry Panchenko Pdf

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.

Author : Anonim
Publisher : Springer
Page : 170 pages
File Size : 45,8 Mb
Release : 2013-02-22
Category : Electronic
ISBN : 1461462908

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The Sherrington-Kirkpatrick Model by Anonim Pdf

Author : Cirano De Dominicis,Irene Giardina
Publisher : Cambridge University Press
Page : 240 pages
File Size : 45,7 Mb
Release : 2006-10-26
Category : Science
ISBN : 0521847834

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Random Fields and Spin Glasses by Cirano De Dominicis,Irene Giardina Pdf

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.

Author : Michel Talagrand
Publisher : Springer Science & Business Media
Page : 608 pages
File Size : 50,8 Mb
Release : 2003-07-11
Category : Computers
ISBN : 3540003568

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Spin Glasses: A Challenge for Mathematicians by Michel Talagrand Pdf

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.

Author : Erwin Bolthausen,Anton Bovier
Publisher : Springer
Page : 190 pages
File Size : 43,7 Mb
Release : 2007-01-11
Category : Science
ISBN : 9783540409083

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Spin Glasses by Erwin Bolthausen,Anton Bovier Pdf

This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.

Author : M Mezard,G Parisi,M Virasoro
Publisher : World Scientific Publishing Company
Page : 476 pages
File Size : 52,6 Mb
Release : 1987-11-01
Category : Science
ISBN : 9789813103917

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Spin Glass Theory and Beyond by M Mezard,G Parisi,M Virasoro Pdf

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.

Author : Michel Talagrand
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 48,9 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9783642152023

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Mean Field Models for Spin Glasses by Michel Talagrand Pdf

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.

Author : Wolfhard Janke
Publisher : Springer
Page : 412 pages
File Size : 41,9 Mb
Release : 2007-12-10
Category : Science
ISBN : 9783540740292

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Rugged Free Energy Landscapes by Wolfhard Janke Pdf

This collection of lectures and tutorial reviews focuses 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. Prominent consideration is given to rugged free-energy landscapes. The authors aim to provide a common basis and technical language for the (computational) technology transfer between the fields and systems considered.

Author : Michael Plischke,Birger Bergersen
Publisher : World Scientific
Page : 540 pages
File Size : 47,6 Mb
Release : 1994
Category : Science
ISBN : 9810216424

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Equilibrium Statistical Physics by Michael Plischke,Birger Bergersen Pdf

This textbook concentrates on modern topics in statistical physics with an emphasis on strongly interacting condensed matter systems. The book is self-contained and is suitable for beginning graduate students in physics and materials science or undergraduates who have taken an introductory course in statistical mechanics. Phase transitions and critical phenomena are discussed in detail including mean field and Landau theories and the renormalization group approach. The theories are applied to a number of interesting systems such as magnets, liquid crystals, polymers, membranes, interacting Bose and Fermi fluids; disordered systems, percolation and spin of equilibrium concepts are also discussed. Computer simulations of condensed matter systems by Monte Carlo-based and molecular dynamics methods are treated.

Author : Hidetoshi Nishimori
Publisher : Clarendon Press
Page : 260 pages
File Size : 40,7 Mb
Release : 2001
Category : Science
ISBN : 0198509413

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Statistical Physics of Spin Glasses and Information Processing by Hidetoshi Nishimori Pdf

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.

Author : Jean Ruiz,Salvador Miracle-sole,Valentin Zagrebnov
Publisher : World Scientific
Page : 554 pages
File Size : 43,9 Mb
Release : 1999-05-14
Category : Electronic
ISBN : 9789814543781

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Mathematical Results In Statistical Mechanics by Jean Ruiz,Salvador Miracle-sole,Valentin Zagrebnov Pdf

This invaluable book is a collection of lectures delivered at the Colloquium 'Mathematical Results in Statistical Mechanics' held in Marseilles, France, on July 27-31, 1998, as a satellite colloquium of the Paris conference STATPHYS 20. It covers a large part of the contemporary results in statistical mechanics, from the point of view of mathematical physics, by leading experts in this field. It includes as the main topics, phase transitions, interfaces, disordered systems, Gibbsian and non-Gibbsian states, as well as recent rigorous treatments in quantum statistical mechanics.

Author : Sergio Albeverio,D Merlini,U Cattaneo
Publisher : World Scientific
Page : 758 pages
File Size : 41,9 Mb
Release : 1995-02-17
Category : Electronic
ISBN : 9789814549691

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Stochastic Processes, Physics And Geometry Ii - Proceedings Of The Iii International Conference by Sergio Albeverio,D Merlini,U Cattaneo Pdf

As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures, and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is concerned with the theory of stochastic processes, quantum theory, and their relations.

Author : James M. Hill,Ross Moore
Publisher : SIAM
Page : 440 pages
File Size : 42,5 Mb
Release : 2004-04-01
Category : Mathematics
ISBN : 0898715598

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Applied Mathematics Entering the 21st Century by James M. Hill,Ross Moore Pdf

Included in this volume are the Invited Talks given at the 5th International Congress of Industrial and Applied Mathematics. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee. This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets. Many papers are direct products of the computer revolution: grid generation, multi-scale modeling, high-dimensional numerical integration, nonlinear optimization, accurate floating-point computations and advanced iterative methods. Other papers demonstrate the close dependence on developments in mathematics itself, and the increasing importance of statistics. Additional topics relate to the study of properties of fluids and fluid-flows, or add to our understanding of Partial Differential Equations.

Author : Anton Bovier,Pierre Picco
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241027

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Mathematical Aspects of Spin Glasses and Neural Networks by Anton Bovier,Pierre Picco Pdf

Author : Manfred Opper,David Saad
Publisher : MIT Press
Page : 300 pages
File Size : 44,6 Mb
Release : 2001
Category : Computers
ISBN : 0262150549

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Advanced Mean Field Methods by Manfred Opper,David Saad Pdf

This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.