Spin Glasses and Complexity

By: Daniel L. Stein, Charles M. Newman

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Paperback | 15 January 2013

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336 Pages

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21.5 x 13.9 x 2.54

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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.

Industry Reviews

"The challenge that Stein and Newman faced in creating this book ... was to write for a broad range of readers and still offer interesting depth. As they state in the preface, they are aiming for a reading level that is between Scientific American and research journals. This reviewer believes they have succeeded... Stein and Newman write well and keep the mathematics to a minimum."--Choice "Stein and Newman have written an excellent introduction to the field of spin glasses and the many ramifications of spin glass theory outside of condensed matter physics and statistical mechanics. Experts and novices alike will find this book interesting and useful."--Jonathan Machta, Statistical Physics

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Non-Fiction Science Physics Materials & States of Matter Mathematics Calculus & Mathematical Analysis Complex Analysis Electricity Applied Mathematics Chaos Theory Nonlinear Science

Preface	p. xi
Introduction: "Why Spin Glasses?	p. 1
Order, Symmetry, and the Organization of Matter	p. 45
The Symmetry of Physical Laws	p. 17
The Hamiltonian	p. 23
Broken Symmetry	p. 26
The Order Parameter	p. 31
Phases of Matter	p. 35
Phase Transitions	p. 39
Summary: The Unity of Condensed Matter Physics	p. 41
Glasses and Quenched Disorder	p. 43
Equilibrium and Nonequilibrium	p. 43
The Glass Transition	p. 45
Localization	p. 49
Magnetic Systems	p. 51
Spin	p. 51
Magnetism in Solids	p. 53
The Paramagnetic Phase	p. 55
Magnetization	p. 55
The Ferromagnetic Phase and Magnetic Susceptibility	p. 57
The Antiferromagnetic Phase	p. 59
Broken Symmetry and the Heisenberg Hamiltonian	p. 59
Spin Glasses: General Features	p. 63
Dilute Magnetic Alloys and the Kondo Effect	p. 64
A New State of Matter?	p. 65
Nonequilibrium and Dynamical Behavior	p. 71
Mechanisms Underlying Spin Glass Behavior	p. 74
The Edwards-Anderson Hamiltonian	p. 78
Frustration	p. 81
Dimensionality and Phase Transitions	p. 83
Broken Symmetry and the Edwards-Anderson Order Parameter	p. 85
Energy Landscapes and Metastability	p. 86
The Infinite-Range Spin Glass	p. 90
Mean Field Theory	p. 90
The Sherrington-Kirkpatrick Hamiltonian	p. 92
A Problem Arises	p. 93
The Remedy	p. 95
Thermodynamic States	p. 97
The Meaning of Replica Symmetry Breaking	p. 98
The Big Picture	p. 109
Applications to Other Fields	p. 112
Computational Time Complexity and Combinatorial Optimization	p. 113
Neural Networks and Neural Computation	p. 129
Protein Folding and Conformational Dynamics	p. 144
Short Takes	p. 168
Short-Range Spin Glasses: Some Basic Questions	p. 175
Ground States	p. 177
Pure States	p. 188
Scenarios for the Spin Glass Phase of the EA Model	p. 193
The Replica Symmetry Breaking and Droplet/Scaling Scenarios	p. 194
The Parisi Overlap Distribution	p. 197
Self Averaging and Non-Self-Averaging	p. 199
Ruling Out the Standard RSB Scenario	p. 201
Chaotic Size Dependence and Metastates	p. 203
A New RSB Scenario	p. 206
Two More (Relatively) New Scenarios	p. 211
Why Should the SK Model Behave Differently from the EA Model?	p. 214
Summary: Where Do We Stand?	p. 216
Are Spin Glasses Complex Systems?	p. 218
Three Foundational Papers	p. 219
Spin Glasses as a Bridge to Somewhere	p. 227
Modern Viewpoints on Complexity	p. 228
Spin Glasses: Old, New, and Quasi-Complexity	p. 233
Notes	p. 239
Glossary	p. 265
Bibliography	p. 285
Index	p. 309
Table of Contents provided by Ingram. All Rights Reserved.

Spin Glasses and Complexity

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Paperback

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