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Theory of Simple Glasses: Exact Solutions in Infinite Dimensions [Kietas viršelis]

5.00/5 (2 ratings by Goodreads)
(Universitą degli Studi di Roma 'La Sapienza', Italy), (Ecole Normale Supérieure, Paris),
  • Formatas: Hardback, 349 pages, aukštis x plotis x storis: 253x178x20 mm, weight: 810 g, Worked examples or Exercises; 3 Tables, black and white; 6 Halftones, black and white; 42 Line drawings, black and white
  • Išleidimo metai: 09-Jan-2020
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107191076
  • ISBN-13: 9781107191075
Kitos knygos pagal šią temą:
Theory of Simple Glasses: Exact Solutions in Infinite DimensionsDidesnis paveikslėlis
  • Formatas: Hardback, 349 pages, aukštis x plotis x storis: 253x178x20 mm, weight: 810 g, Worked examples or Exercises; 3 Tables, black and white; 6 Halftones, black and white; 42 Line drawings, black and white
  • Išleidimo metai: 09-Jan-2020
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107191076
  • ISBN-13: 9781107191075
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107191075.html
Raktažodžiai:
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.

Recenzijos

'In this advanced textbook, the authors, all solid-state physicists, present a theory of simple glasses, defined as collections of interacting point particles. The approach, based on statistical mechanics and concepts of multiple-state metastability, is rigorous and educational. Derivations are careful and detailed An especially useful and educational feature is that each chapter includes a résumé of main results and an annotated short bibliography geared to beginning students. An extensive, up-to-date bibliography at the end mainly draws from the Physical Review literature and related journals. Minimally indexed (no entries on shear stress or strain, viscosity, temperature, or spheres), the book is oriented toward advanced undergraduates or beginning graduate students (who will need preparation in statistical mechanics and liquid theory) and researchers in glasses, essentially addressing the solid-state physics and statistical mechanics communities.' J. Lambropoulos, Choice

Daugiau informacijos

A self-contained book describing the modern mean field theory of simple structural glasses using a quantum statistical mechanical approach.
Preface ix
1 Infinite-Dimensional Models in Statistical Physics
1(36)
1.1 The Ising Model
1(5)
1.2 Large Dimension Expansion for the Ising Model
6(4)
1.3 Second-Order Phase Transition of the Ising Ferromagnet
10(8)
1.4 Low-Temperature Ferromagnetic Phase
18(8)
1.5 Metastable States
26(8)
1.6 Wrap-Up
34(3)
2 Atomic Liquids in Infinite Dimensions: Thermodynamics
37(30)
2.1 Thermodynamics of Atomic Systems
37(9)
2.2 The Virial Expansion
46(4)
2.3 Liquids in Large Dimensions
50(12)
2.4 Wrap-Up
62(2)
2.5 Appendix: Rotationally Invariant Integrals
64(3)
3 Atomic Liquids in Infinite Dimensions: Equilibrium Dynamics
67(32)
3.1 Properties of Equilibrium Dynamics
68(8)
3.2 Langevin Dynamics of Liquids in Infinite Dimensions
76(6)
3.3 Dynamical Glass Transition
82(7)
3.4 Critical Properties of the Dynamical Glass Transition
89(4)
3.5 Wrap-Up
93(4)
3.6 Appendix: Reversibility for Langevin Dynamics
97(2)
4 Thermodynamics of Glass States
99(41)
4.1 Arrested Dynamics and Restricted Thermodynamics
99(10)
4.2 Restricted Thermodynamics in Infinite Dimensions
109(11)
4.3 Replicated Free Energy and Replica Symmetry
120(8)
4.4 Replica Symmetric Phase Diagram of Simple Glasses
128(4)
4.5 Wrap-Up
132(3)
4.6 Appendix
135(5)
5 Replica Symmetry Breaking and Hierarchical Free Energy Landscapes
140(40)
5.1 An Introduction to Replica Symmetry Breaking
140(6)
5.2 The Algebra of Hierarchical Matrices
146(8)
5.3 Probability Distribution of the Mean Square Displacement
154(10)
5.4 Replicated Free Energies and Hierarchical Matrices
164(8)
5.5 De Almeida-Thouless Transition and Marginal Stability
172(4)
5.6 Wrap-Up
176(4)
6 The Gardner Transition
180(19)
6.1 State Following in the Replica Symmetry Broken Phase
180(5)
6.2 Gardner Transition and Replica Symmetry Breaking
185(2)
6.3 Gardner Transition of Simple Glasses
187(6)
6.4 Critical Properties of the Gardner Transition
193(2)
6.5 Wrap-Up
195(2)
6.6 Appendix: Numerical Resolution of the RSB Equations
197(2)
7 Counting Glass States: The Complexity
199(32)
7.1 Equilibrium Complexity and the Kauzmann Temperature
199(5)
7.2 Out-of-Equilibrium Complexity: The Monasson Method
204(6)
7.3 The Monasson Construction in Infinite Dimensions
210(4)
7.4 The Phase Diagram of Hard Spheres
214(8)
7.5 Replica Symmetry Breaking Instability in the Monasson Construction
222(5)
7.6 Wrap-Up
227(4)
8 Packing Spheres in Large Dimensions
231(20)
8.1 Statement of the Problem
231(4)
8.2 Review of Rigorous Results
235(5)
8.3 Review of Non-rigorous Results
240(3)
8.4 Liquid, Glass and Packings in Infinite Dimensions
243(5)
8.5 Wrap-Up
248(3)
9 The Jamming Transition
251(39)
9.1 The Jamming Transition as a Satisfiability Threshold
251(9)
9.2 Criticality of Jamming
260(13)
9.3 The Unjammed Phase: Hard Spheres
273(7)
9.4 The Overjammed Phase: Soft Harmonic Spheres
280(7)
9.5 Wrap-Up
287(3)
10 Rheology of the Glass
290(15)
10.1 Perturbing the Glass by a Shear Strain
290(5)
10.2 Linear Response
295(4)
10.3 Stress-Strain Curves
299(3)
10.4 Wrap-Up
302(3)
References 305(17)
Index 322
Giorgio Parisi is a Professor of Physics at the Universitą degli Studi di Roma 'La Sapienza', Italy. His research is broadly focused on theoretical physics; from particle physics to glassy systems. He has been the recipient of numerous awards, including the Boltzmann Medal, the Enrico Fermi Prize, the Max Planck Medal, the Lars Onsager Prize and an ERC advanced grant. He is president of the Accademia dei Lincei and a member of the collaboration 'Cracking the glass problem', funded by the Simons Foundation. Pierfrancesco Urbani is a CNRS researcher. His research activity focuses on statistical physics of disordered and glassy systems. After a joint Ph.D. between Sapienza University of Rome, Italy and Université Paris-Sud, France, he joined the Institut de Physique Théorique of CEA, first as a post-doctoral researcher and then as a permanent researcher. Francesco Zamponi is a Centre national de la recherche scientifique (CNRS) Research Director and an Associated Professor at Ecole Normale Supérieure, Paris. His research is broadly focused on complex systems, ranging from glasses to agent-based models for macroeconomy. He has been awarded an ERC consolidator research grant and he is a member of the collaboration 'Cracking the glass problem' funded by the Simons Foundation.