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Spin Glasses and Complexity
Daniel L. Stein & Charles M. Newman

Book Description | Reviews
Introduction [in PDF format]

TABLE OF CONTENTS:

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

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File created: 11/11/2014

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