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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.
Preface xi
Introduction: Why Spin Glasses? 1
1. Order, Symmetry, and the Organization of Matter 15
2. Glasses and Quenchied Disorder 43
3. Magnetic Systems 51
4. Spin Glasses: General Features 63
5. The Infinite-Range Spin Glass 90
6. Applications to Other Fields 112
7. Short-Range Spin Glasses: Some Basic Questions 175
8. Are Spin Glasses Complex Systems? 218
Notes 239
Glossary 265
Bibliography 285
Index 309
Daniel L. Stein is a professor of physics and mathematics at New York University's Courant Institute of Mathematical Sciences. His books include Spin Glasses and Biology.
Charles M. Newman is a professor of mathematics at NYU's Courant Institute of Mathematical Sciences and at the University of California, Irvine. His books include Topics in Disordered Systems.
"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
"[A] surprisingly broad field of view is visible through the lens of the classical, equilibrium using spin glass and the authors are able to use it to explore many fascinating topics. 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, Journal of Statistical Physics
"Spin Glasses and Complexity is not a journalistic book that merely reports on the subject. Based on profound mathematical insights, here distilled into an incisive presentation, it represents the fruit of the lifelong commitments two experts have made to spin-glass theory within and beyond physics [...] Spin Glasses and Complexity is unique in successfully bringing this thrilling theme to a broader scientific audience."
– Stefan Boettcher, Physics Today
"[T]he work is well presented and the reader will surely find it both inspiring and interesting."
– Marco Castrillon Lopez, European Mathematical Society
