Spin Glasses and Complexity Book

Preface xi

Introduction: Why Spin Glasses? 1

• 1. Order, Symmetry, and the Organization of Matter 15
• 1.1 The Symmetry of Physical Laws 17
• 1.2 The Hamiltonian 23
• 1.3 Broken Symmetry 26
• 1.4 The Order Parameter 31
• 1.5 Phases of Matter 35
• 1.6 Phase Transitions 39
• 1.7 Summary: The Unity of Condensed Matter Physics 41

2. Glasses and Quenchied Disorder 43

• 2.1 Equilibrium and Non Equilibrium 43
• 2.2 The Glass Transition 45
• 2.3 Localization 49
  

3. Magnetic Systems 51

• 3.1 Spin 51
• 3.2 Magnetism in Solids 53
• 3.3 The Paramagnetic Phase 55
• 3.4 Magnetization 55
• 3.5 The Ferromagnetic Phase and Magnetic Susceptibility 57
• 3.6 The Antiferromagnetic Phase 59
• 3.7 Broken Symmetry and the Heisenberg Hamiltonian 59
  

4. Spin Glasses: General Features 63

• 4.1 Dilute Magnetic Alloys and the Kondo Effect 64
• 4.2 A New State of Matter? 65
• 4.3 Nonequilibrium and Dynamical Behavior 71
• 4.4 Mechanisms Underlying Spin Glass Behavior 74
• 4.5 The Edwards-Anderson Hamiltonian 78
• 4.6 Frustration 81
• 4.7 Dimensionality and Phase Transitions 83
• 4.8 Broken Symmetry and the Edwards-Anderson Order Parameter 85
• 4.9 Energy Landscapes and Metastability 86
  

5. The Infinite-Range Spin Glass 90

• 5.1 Mean Field Theory 90
• 5.2 The Sherrington-Kirkpatrick Hamiltonian 92
• 5.3 A Problem Arises 93
• 5.4 The Remedy 95
• 5.5 Thermodynamic States 97
• 5.6 The Meaning of Replica Symmetry Breaking 98
• 5.7 The Big Picture 109
  

6. Applications to Other Fields 112

• 6.1 Computational Time Complexity and Combinatorial Optimization 113
• 6.2 Neural Networks and Neural Computation 129
• 6.3 Protein Folding and Conformational Dynamics 144
• 6.4 Short Takes 168
  

7. Short-Range Spin Glasses: Some Basic Questions 175

• 7.1 Ground States 177
• 7.2 Pure States 188
• 7.3 Scenarios for the Spin Glass Phase of the EA Model 193
• 7.4 The Replica Symmetry Breaking and Droplet/Scaling Scenarios 194
• 7.5 The Parisi Overlap Distribution 197
• 7.6 Self-Averaging and Non-Self-Averaging 199
• 7.7 Ruling Out the Standard RSB Scenario 201
• 7.8 Chaotic Size Dependence and Metastates 203
• 7.9 A New RSB Scenario 206
• 7.10 Two More (Relatively) New Scenarios 211
• 7.11 Why Should the SK Model Behave Differently from the EA Model? 214
• 7.12 Summary: Where Do We Stand? 216
  

8. Are Spin Glasses Complex Systems? 218

• 8.1 Three Foundational Papers 219
• 8.2 Spin Glasses as a Bridge to Somewhere 227
• 8.3 Modern Viewpoints on Complexity 228
• 8.4 Spin Glasses: Old, New, and Quasi-Complexity 233

Notes 239

Glossary 265

Bibliography 285

Index 309