Spin Glasses and Complexity, Daniel L. Stein and Charles M. Newman, Princeton U. Press, 2013. $39.95 (317 pp.). ISBN 978-0-691-14733-8 paper
The ideas and concepts that originated with the study of spin glasses have pervaded many seemingly unrelated fields, including biology, communications, economics, computer science, and engineering. Indeed, practitioners in specific disciplines who employ spin-glass concepts are often unaware of their scope and generality; many are not even aware that they are “consumers.” For instance, many inverse problems in today’s big-data environment involve the analysis of correlation matrices of excitatory and inhibitory couplings between large numbers of variables; such problems have exactly the form of a disordered bond matrix connecting spins in a glass.
If your problems involve a large number of coupled variables, chances are that you could benefit from learning about spin-glass theory. That’s generally a daunting mathematical task, made palpable with an intuitive but no less logical approach in Daniel Stein and Charles Newman’s Spin Glasses and Complexity. I highly recommend this book to any reader with a scientific interest in disorder or complexity.
Stein and Newman succeed in translating into plain language a subject that can seem esoteric, and they convincingly argue its importance for those who study complexity in any discipline. The discussion is put carefully within reach of a scientifically literate audience. Unlike conventional popularizations, it deals with profound concepts in depth and does not shy away from, say, exhibiting a spin-glass Hamiltonian in an equation or describing the impact of bond distributions.
The authors’ focused and emphatic style pulls readers in and guides them along. Well-placed summary and overview paragraphs—frequently starting with “Let’s review what we have so far”—orient the reader before the next line of argument commences. Apart from the 240-page text, some 30 pages of notes, a 20-page glossary, and 300 references to primary sources and books for more in-depth study unclutter the main thrust of the story.
The authors start with the question of why even a physicist would care about the humble spin glass, with its rather undistinguished electronic characteristics and, of late, little experimental interest. Unlike other esoteric subjects, such as black holes, a spin glass doesn’t have the flash that immediately captures the imagination. Yet, its efficient display of experimentally observed aspects of disorder has inspired some fundamental questions about our understanding of materials and the universality concept for phase transitions. While pedagogically linking glasses to complexity in the first four chapters, the authors also lay the groundwork for the claim that statistical physics is indispensable for dealing with complex systems that typically have a large number of variables.
The inevitable turn to the Sherrington–Kirkpatrick spin glass and replicas in chapter 5 may seem disconcerting to the uninitiated reader. But the authors never lose sight of the big picture: They subsequently relate the mean-field concepts developed in that chapter to a range of complex problems, like the traveling salesperson, neural networks, and protein folding. Naturally, the authors present their interpretation of finite-dimensional spin glasses. They confine that discussion to chapter 7, which explores the poorly understood nature of the finite-dimensional spin glass and its relation to the rich features derived from Giorgio Parisi’s exact mean-field solution. It is a challenging chapter, but it does not distract from the book’s overall flow.
The concluding eighth chapter is a philosophical discourse on complexity, infused with historical references. In it, the authors make a compelling case for a deep connection between the hallmark features of spin glasses—disorder, constraints, frustration, and hierarchies—and our still tenuous attempts to identify the underlying principles of complexity. They posit the spin glass as a constitutive model of complex behavior, analogous to the Ising model for critical behavior.
Because it would have exploded the size of the book, the discussion of nonequilibrium dynamics is decidedly brief. The behavior we observe for real-world complex systems is rarely in equilibrium, with poorly understood consequences; little can be said even for the model spin glass. More significant is the book’s dearth of contemporary examples of the evermore widespread application of the mean-field replica theory to communications, inference, data analysis, and algorithm development. As those topics relate directly to the everyday big-data concerns of a large potential readership, their scant mention understates the present impact of spin-glass theory.
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. Some nice textbooks and technical reviews already exist to introduce students to the subject, but Spin Glasses and Complexity is unique in successfully bringing this thrilling theme to a broader scientific audience.
Stefan Boettcher is an associate professor of physics at Emory University in Atlanta, Georgia. His interests include the theory and simulation of disordered systems, nonequilibrium dynamics, and phase transitions.
