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Spin Glasses: A Challenge for Mathematicians

2003-07-11 Computers
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Release : 2003-07-11
Genre : Computers
Kind : eBook
Book Rating : 564/5 ( reviews)

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Book Synopsis Spin Glasses: A Challenge for Mathematicians by : Michel Talagrand

Download or read book Spin Glasses: A Challenge for Mathematicians written by Michel Talagrand. This book was released on 2003-07-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spin Glasses and Complexity

2013-01-15 Science
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Release : 2013-01-15
Genre : Science
Kind : eBook
Book Rating : 637/5 ( reviews)

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Book Synopsis Spin Glasses and Complexity by : Daniel L. Stein

Download or read book Spin Glasses and Complexity written by Daniel L. Stein. This book was released on 2013-01-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mean Field Models for Spin Glasses

2011 Spin glasses
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Release : 2011
Genre : Spin glasses
Kind : eBook
Book Rating : 030/5 ( reviews)

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Book Synopsis Mean Field Models for Spin Glasses by : Michel Talagrand

Download or read book Mean Field Models for Spin Glasses written by Michel Talagrand. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:

The Sherrington-Kirkpatrick Model

2013-02-26 Mathematics
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Release : 2013-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 894/5 ( reviews)

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Book Synopsis The Sherrington-Kirkpatrick Model by : Dmitry Panchenko

Download or read book The Sherrington-Kirkpatrick Model written by Dmitry Panchenko. This book was released on 2013-02-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mean Field Models for Spin Glasses

2011-08-14 Mathematics
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Release : 2011-08-14
Genre : Mathematics
Kind : eBook
Book Rating : 536/5 ( reviews)

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Book Synopsis Mean Field Models for Spin Glasses by : Michel Talagrand

Download or read book Mean Field Models for Spin Glasses written by Michel Talagrand. This book was released on 2011-08-14. Available in PDF, EPUB and Kindle. Book excerpt: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). 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 present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.

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