Spin Glasses and Complexity

Spin Glasses and Complexity

Daniel L. Stein
Charles M. Newman
Copyright Date: 2013
Pages: 368
https://www.jstor.org/stable/j.ctt12f4hf
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  • Book Info
    Spin Glasses and Complexity
    Book Description:

    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 Complexityoffers 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 Complexityalso 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.

    eISBN: 978-1-4008-4563-7
    Subjects: Mathematics, General Science

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. PREFACE
    (pp. xi-xviii)
  4. INTRODUCTION: WHY SPIN GLASSES?
    (pp. 1-14)

    Spin glasses are disordered magnetic materials, and it’s hard to find a less promising candidate to serve as a focal point of complexity studies, much less as the object of thousands of investigations. On first inspection, they don’t seem particularly exciting. Although they’re a type of magnet, they’re not very good at being magnetic. Metallic spin glasses are unremarkable conductors, and insulating spin glasses are fairly useless as practical insulators. So why the interest?

    Well, the answer to that depends on where you’re coming from. In what follows we’ll explore those features of spin glasses that have attracted, in turn,...

  5. 1 ORDER, SYMMETRY, AND THE ORGANIZATION OF MATTER
    (pp. 15-42)

    Quarks, strings, and black holes receive much of the attention that the popular press devotes to physics, and for good reason: they’re exciting, exotic, and almost mystical in their appeal. They’re also comfortably removed from the everyday world around us. We may be ultimately composed of vibrating stringlike excitations, and black holes may govern the history and future of the universe we live in, but for most of us, their impact on our daily lives is nil.

    Does that mean that these subjects are of no real value, aside from providing intellectual entertainment for some (and for a very few,...

  6. 2 GLASSES AND QUENCHED DISORDER
    (pp. 43-50)

    When we discussed in section 1.6 the discontinuous behavior of thermodynamic functions at a phase transition, we referred (somewhat obliquely) to “carefully controlled conditions.” To proceed to the next part of our story, we need to explain just what we meant by this. To do so, we turn to the central notion ofthermodynamic equilibrium.

    The goal of thermodynamics is to obtain as economical a description as possible of a macroscopic system comprising a huge collection of interacting atomic- or subatomic-sized units. A glass of water consists of order 10²⁴ water molecules; how do we describe its physical state? What...

  7. 3 MAGNETIC SYSTEMS
    (pp. 51-62)

    Up to this point our discussion has centered on some basic concepts of condensed matter physics as viewed through the illustrative lenses of familiar systems: liquids, crystals, and glasses. We now turn to another important class of materials: magnetic systems, which we’ll regard as materials possessing properties that can be altered or manipulated through the application of an external magnetic field.

    Of course, these categories overlap: a magnet can be crystalline or glassy, solid or liquid. What’s really changing is our focus on the behaviors we’d like to understand. The same piece of iron might be of interest to some...

  8. 4 SPIN GLASSES: GENERAL FEATURES
    (pp. 63-89)

    As noted in the introduction, few things seem less likely at first glance to spark interest than the materials we now call spin glasses. Nevertheless, their rise was stunning. What one might call “sightings” of spin glasses, although they weren’t realized as such at the time, appeared sporadically in the scientific literature over several decades spanning the middle part of the twentieth century (see, e.g. [49–51]). But it wasn’t until the early 1970s that the condensed matter community first took serious notice of them, as a set of peculiar materials with perplexing and seemingly self-contradictory properties. Within a few...

  9. 5 THE INFINITE-RANGE SPIN GLASS
    (pp. 90-111)

    We saw in section 1.5 how, given a Hamiltonian and using the tools of statistical mechanics, one can—in principle—completely describe a system’s thermodynamic behavior at any temperature or external field. In practice, however, this is extremely difficult; if it weren’t, statistical mechanics would be a closed book rather than a thriving field of active research. Very few Hamiltonians can be exactly “solved,” meaning that the corresponding free energy as a function of temperature, magnetic field, and so on, can be exactly calculated. In spite of this, the thermodynamic properties of a tremendous number of physical systems have been...

  10. 6 APPLICATIONS TO OTHER FIELDS
    (pp. 112-174)

    We’ve already encountered more than a few surprises yielded up by spin glass research. But perhaps none is so great as its unanticipated impact on an impressive array of problems from other fields. Mathematical and conceptual tools developed for spin glasses have found their way into a variety of applications, including the introduction of new methods for obtaining estimates on optimal solutions of computationally “hard” problems; the development of new algorithms with broad-based applicability; the development of new methods for biologically based computation; the develpoment of new models of neural networks, protein dynamics and folding, prebiotic evolution, and maturation of...

  11. 7 SHORT-RANGE SPIN GLASSES: SOME BASIC QUESTIONS
    (pp. 175-217)

    In this chapter we consider realistic spin glass models, in particular the Edwards-Anderson (EA) model introduced in section 4.5. Both the EA and the Sherrington-Kirkpatrick (SK) models are idealizations of the complicated spatial structure of spin-spin interactions in real materials, as discussed in section 4.4. In the EA idealization, the interactions are extremely short range, occurring only between spins that are nearest neighbors in the atomic lattice. This caricatures the actual spatial structure of laboratory spin glasses, but the EA model is nevertheless believed to distill their essential physics.

    In contrast, the SK model is bereft of geometric structure and,...

  12. 8 ARE SPIN GLASSES COMPLEX SYSTEMS?
    (pp. 218-238)

    We conclude our primer with a brief consideration of how spin glass science fits into the larger area of complexity studies. As putative complex systems, spin glasses are unusual in that they fall neatly into standard, well-defined disciplinary categories: condensed matter physics and statistical mechanics. That concepts and techniques arising from their study served usefully in other disciplines was initially an unanticipated bonus. Be that as it may, these applications have come to define the field as much as its original, narrower domain. The fact that a significant number of nonphysicists and nonmathematicians are even aware of spin glasses, regardless...

  13. NOTES
    (pp. 239-264)
  14. GLOSSARY
    (pp. 265-284)
  15. BIBLIOGRAPHY
    (pp. 285-308)
  16. INDEX
    (pp. 309-317)