Glassy Materials and Disordered Solids : An Introduction to Their Statistical Mechanics

by Binder, Kurt; Kob, Walter

• ISBN13: 9789812565105
• ISBN10: 9812565108
• Format: Hardcover
• Copyright: 2005-12-30
• Publisher: World Scientific Pub Co Inc

Summary

The physics of glassy materials and disordered solids presents students with an area of study much more challenging than the physics of crystalline solids. Written by two recognized experts in the field, this highly readable book tackles the subject with the student firmly in mind, beginning with a pedagogical introduction to important concepts such as percolation, fractals, spin glasses, and glasses. Making use of these concepts, the authors show that such systems share many common aspects that can be described within the framework of statistical mechanics. The book is also an essential standard text for researchers on amorphous materials, equally accessible for theorists and experimentalists.

Table of Contents

Preface	p. v
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. 63
Models of Disordered Structures	p. 79
Random Walks: A Simple Model for the Configurations of Flexible Polymers	p. 79
Percolation: A First Example of a Fractal Structure	p. 94
The Percolation Probability and Percolation Threshold	p. 94
Diluted Magnets and Critical Exponents	p. 98
The Fractal Dimensionality and the Concept of Finite Size Scaling	p. 104
Scaling of the Cluster Size Distribution	p. 106
Percolation for Low and High Lattice Dimensions	p. 109
Rigidity Percolation	p. 113
Other Fractals (Diffusion-Limited Aggregation, Random Surfaces, etc.)	p. 116
General Concepts on Fractal Geometry	p. 116
Diffusion-Limited Aggregation	p. 120
Growth of Random Interfaces	p. 122
Random Close Packing	p. 124
Continuous Random Networks	p. 132
Chemically Realistic Models of Structural Glasses	p. 139
General Concepts and Physical Properties of Disordered Matter	p. 165
The Rouse Model for Polymer Dynamics: A Simple Example for the Consequences of the Random Walk Picture	p. 165
Application of the Percolation Problem to Physical Systems	p. 178
Percolation Conductivity and a Naive Treatment of the Elasticity of Polymer Networks	p. 178
Excitations of Diluted Magnets Near the Percolation Threshold	p. 183
Effective Medium Theory	p. 188
Elementary Excitations of Fractal Structures	p. 190
Diffusion on a Percolation Cluster: The "Ant in the Labyrinth"	p. 190
The Spectral Dimension and Fracton Excitations	p. 193
The Sol-Gel Transition Revisited	p. 198
Physical Properties of Amorphous Solids	p. 202
Two-Level Systems	p. 203
Anomalies of Glasses at Intermediate Temperatures: Excess Specific Heat, Thermal Conductivity Plateau, and Boson Peak	p. 210
Spin Glasses	p. 221
Some Experimental Facts about Spin Glasses: Systems and Physical Properties	p. 222
Theoretical Models	p. 233
The Replica Method and the Mean Field Theory of the Ising Spin Glass	p. 237
Replica Symmetry Breaking	p. 245
Spin Glasses Beyond Mean Field Theory	p. 255
Variants and Extensions of Spin Glasses	p. 263
p-Spin Interaction Spin Glasses and the Random Energy Model	p. 263
Potts Glasses	p. 264
Quadrupolar Glasses as Models for Diluted Molecular Crystals	p. 276
Atomistically Realistic Models of Diluted Molecular Crystals	p. 281
Spin Models with Quenched Random Fields	p. 285
Supercooled Liquids and the Glass Transition	p. 311
Phenomenology of Glass-Forming Systems	p. 312
Models for Slow Relaxation	p. 331
The Theory of Adam and Gibbs	p. 332
The Free Volume Theory	p. 338
Kinetically Constrained Models	p. 345
The Mode-Coupling Theory of the Glass Transition	p. 359
The Zwanzig-Mori Projection Operator Formalism	p. 360
The Mode-Coupling Approximations	p. 364
The Mode-Coupling Theory of the Glass Transition	p. 366
Predictions of Mode-Coupling Theory	p. 375
The Relaxation Dynamics of Glass-Forming Liquids and Test of the Predictions of MCT	p. 385
Concluding Remarks on Mode-Coupling Theory	p. 412
Index	p. 431
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