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Zusatztext "Well presented and the reader will surely find it both inspiring and interesting." ---Marco Castrillon Lopez, European Mathematical Society Informationen zum Autor Daniel L. Stein & Charles M. Newman Klappentext "This excellent book fills a unique and valuable niche. It is a great introduction to some fascinating physics, emphasizing the fundamental concepts and the connections to other complex systems. There are lots of technical volumes on spin glasses, but no other book works at this nonmathematical level, certainly not while still being so accurate and insightful." --Cosma Shalizi, Carnegie Mellon University "This primer builds the theory of spin glasses, starting with the real physical systems and experiments that inspired the theory. Stein and Newman work hard to make this material accessible to nonphysicists, and they write in an entertaining and friendly way. Even as a physicist I learned a fair amount." --Cris Moore, Santa Fe Institute Zusammenfassung 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, S pin 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. Inhaltsverzeichnis 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 Co...
