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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 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.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. Introduction: Why Spin Glasses?
  7. 1. Order, Symmetry, and the Organization of Matter
    1. 1.1 The Symmetry of Physical Laws
    2. 1.2 The Hamiltonian
    3. 1.3 Broken Symmetry
    4. 1.4 The Order Parameter
    5. 1.5 Phases of Matter
    6. 1.6 Phase Transitions
    7. 1.7 Summary: The Unity of Condensed Matter Physics
  8. 2. Glasses and Quenched Disorder
    1. 2.1 Equilibrium and Nonequilibrium
    2. 2.2 The Glass Transition
    3. 2.3 Localization
  9. 3. Magnetic Systems
    1. 3.1 Spin
    2. 3.2 Magnetism in Solids
    3. 3.3 The Paramagnetic Phase
    4. 3.4 Magnetization
    5. 3.5 The Ferromagnetic Phase and Magnetic Susceptibility
    6. 3.6 The Antiferromagnetic Phase
    7. 3.7 Broken Symmetry and the Heisenberg Hamiltonian
  10. 4. Spin Glasses: General Features
    1. 4.1 Dilute Magnetic Alloys and the Kondo Effect
    2. 4.2 A New State of Matter?
    3. 4.3 Nonequilibrium and Dynamical Behavior
    4. 4.4 Mechanisms Underlying Spin Glass Behavior
    5. 4.5 The Edwards-Anderson Hamiltonian
    6. 4.6 Frustration
    7. 4.7 Dimensionality and Phase Transitions
    8. 4.8 Broken Symmetry and the Edwards-Anderson Order Parameter
    9. 4.9 Energy Landscapes and Metastability
  11. 5. The Infinite-Range Spin Glass
    1. 5.1 Mean Field Theory
    2. 5.2 The Sherrington-Kirkpatrick Hamiltonian
    3. 5.3 A Problem Arises
    4. 5.4 The Remedy
    5. 5.5 Thermodynamic States
    6. 5.6 The Meaning of Replica Symmetry Breaking
    7. 5.7 The Big Picture
  12. 6. Applications to Other Fields
    1. 6.1 Computational Time Complexity and Combinatorial Optimization
    2. 6.2 Neural Networks and Neural Computation
    3. 6.3 Protein Folding and Conformational Dynamics
    4. 6.4 Short Takes
  13. 7. Short-Range Spin Glasses: Some Basic Questions
    1. 7.1 Ground States
    2. 7.2 Pure States
    3. 7.3 Scenarios for the Spin Glass Phase of the EA Model
    4. 7.4 The Replica Symmetry Breaking and Droplet/Scaling Scenarios
    5. 7.5 The Parisi Overlap Distribution
    6. 7.6 Self-Averaging and Non-Self-Averaging
    7. 7.7 Ruling Out the Standard RSB Scenario
    8. 7.8 Chaotic Size Dependence and Metastates
    9. 7.9 A New RSB Scenario
    10. 7.10 Two More (Relatively) New Scenarios
    11. 7.11 Why Should the SK Model Behave Differently from the EA Model?
    12. 7.12 Summary: Where Do We Stand?
  14. 8. Are Spin Glasses Complex Systems?
    1. 8.1 Three Foundational Papers
    2. 8.2 Spin Glasses as a Bridge to Somewhere
    3. 8.3 Modern Viewpoints on Complexity
    4. 8.4 Spin Glasses: Old, New, and Quasi-Complexity
  15. Notes
  16. Glossary
  17. Bibliography
  18. Index