Glassy Materials and Disordered Solids : An Introduction to their Statistical Mechanics (Revised Edition)

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ISBN: 9789814350174 | 9814350176
Cover: Hardcover
Copyright: 1/26/2011

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This book gives a pedagogical introduction to the physics of amorphous solids and related disordered condensed matter systems. Important concepts from statistical mechanics such as percolation, random walks, fractals and spin glasses are explained. Using these concepts, the common aspects of these systems are emphasized, and the current understanding of the glass transition and the structure of glasses are concisely reviewed. This second edition includes new material on emerging topics in the field of disordered systems such as gels, driven systems, dynamical heterogeneities, growing length scales etc. as well as an update of the literature in this rapidly developing field.

Preface	p. vii
Preface to the second edition	p. ix
Introduction	p. 1
Models of Disordered Matter: A Brief Overview	p. 1
General Concepts on the Statistical Mechanics of Disordered Matter	p. 13
Lattice Models	p. 13
Averaging in Random Systems: Quenched versus Annealed Disorder	p. 17
"Symmetry Breaking'' and "Ergodicity Breaking"	p. 20
Configurational Entropy versus ''Complexity'', and the Kauzmann Paradox	p. 25
Structure and Dynamics of Disordered Matter	p. 35
Pair Distribution Functions and the Static Structure Factor	p. 35
Topological Disorder and Bond Orientational Correlations	p. 51
General Aspects of Dynamic Correlation Functions and Transport Properties	p. 64
Models of Disordered Structures	p. 81
Random Walks: A Simple Model for the Configurations of Flexible Polymers	p. 81
Percolation: A First Example of a Fractal Structure	p. 96
The Percolation Probability and Percolation Threshold	p. 96
Diluted Magnets and Critical Exponents	p. 100
The Fractal Dimensionality and the Concept of Finite Size Scaling	p. 106
Scaling of the Cluster Size Distribution	p. 108
Percolation for Low and High Lattice Dimensions	p. 111
Rigidity Percolation	p. 115
Other Fractals (Diffusion-Limited Aggregation, Random Surfaces, etc.)	p. 118
General Concepts on Fractal Geometry	p. 118
Diffusion-Limited Aggregation	p. 122
Growth of Random Interfaces	p. 124
Random Close Packing	p. 126
Continuous Random Networks	p. 135
Chemically Realistic Models of Structural Glasses	p. 142
Liquid and Solid Foams: Random Cellular Structures	p. 159
General Concepts and Physical Properties of Disordered Matter	p. 173
The Rouse Model for Polymer Dynamics: A Simple Example for the Consequences of the Random Walk Picture	p. 173
Application of the Percolation Problem to Physical Systems	p. 186
Percolation Conductivity and a Naive Treatment of the Elasticity of Polymer Networks	p. 186
Excitations of Diluted Magnets Near the Percolation Threshold	p. 191
Effective Medium Theory	p. 196
Elementary Excitations of Fractal Structures	p. 198
Diffusion on a Percolation Cluster: The ôAnt in the Labyrinth"	p. 198
The Spectral Dimension and Fracton Excitations	p. 201
The Sol-Gel Transition Revisited	p. 206
Physical Properties of Amorphous Solids	p. 211
Two-Level Systems	p. 121
Anomalies of Glasses at Intermediate Temperatures: Excess Specific Heat, Thermal Conductivity Plateau, and Boson Peak	p. 218
Spin Glasses	p. 230
Some Experimental Facts about Spin Glasses: Systems and Physical Properties	p. 231
Theoretical Models	p. 241
The Replica Method and the Mean Field Theory of the Ising Spin Glass	p. 246
Replica Symmetry Breaking	p. 254
Spin Glasses Beyond Mean Field Theory	p. 265
Variants and Extensions of Spin Glasses	p. 276
p-Spin Interaction Spin Glasses and the Random Energy Model	p. 277
Potts Glasses	p. 279
Quadrupolar Glasses as Models for Diluted Molecular Crystals	p. 291
Atomistically Realistic Models of Diluted Molecular Crystals	p. 297
Spin Models with Quenched Random Fields	p. 301
From Spin Glasses to Computer Science and Information: An Outlook to the Random Satisfiability Problem	p. 317
Supercooled Liquids and the Glass Transition	p. 339
Phenomenology of Glass-Forming Systems	p. 340
The Mode Coupling Theory of the Glass Transition	p. 360
The Zwanzig-Mori Projection Operator Formalism	p. 361
The Mode Coupling Approximations	p. 366
The Mode Coupling Theory of the Glass Transition	p. 368
Predictions of Mode Coupling Theory	p. 376
The Relaxation Dynamics of Glass-Forming Liquids and Test of the Predictions of MCT	p. 387
Some General Remarks on Mode Coupling Theory	p. 414
Further Models for Glassy Dynamics; Dynamical Heterogeneities; Gels; Driven Systems	p. 433
Models for Slow Relaxation	p. 433
The Theory of Adam and Gibbs	p. 434
The Free Volume Theory	p. 439
Kinetically Constrained Models	p. 448
Dynamical Heterogeneities and Growing Length Scales	p. 463
Gels versus Glasses	p. 493
Driven Systems	p. 506
Glasses under Shear	p. 506
Aging Dynamics of Glassy Systems	p. 513
Concluding Remarks	p. 516
Index
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Glassy Materials and Disordered Solids : An Introduction to their Statistical Mechanics (Revised Edition)

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