Theory of Simple Glasses: Exact Solutions in Infinite Dimensions

Description

This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics. Cover ......Page 1 Front Matter ......Page 3 THEORY OF SIMPLE GLASSES: Exact Solutions in Infinite Dimensions......Page 5 Copyright ......Page 6 Contents ......Page 7 Preface ......Page 11 1 Infinite-Dimensional Models in Statistical Physics......Page 19 2 Atomic Liquids in Infinite Dimensions Thermodynamics......Page 55 3 Atomic Liquids in Infinite Dimensions Equilibrium Dynamics......Page 85 4 Thermodynamics of Glass States......Page 117 5 Replica Symmetry Breaking and Hierarchical Free Energy Landscapes......Page 158 6 The Gardner Transition......Page 198 7 Counting Glass States The Complexity......Page 217 8 Packing Spheres in Large Dimensions......Page 249 9 The Jamming Transition......Page 269 10 Rheology of the Glass......Page 308 References ......Page 323 Index......Page 340