Patrick Charbonneau & Enzo Marinari 
SPIN GLASS THEORY AND FAR BEYOND [EPUB ebook] 
Replica Symmetry Breaking After 40 Years

About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew the attention of theoretical physicists. It soon became clear that understanding these systems, now called spin glasses, would give rise to a new branch of statistical physics. As physical materials, spin glasses were found to be as useless as they were exotic. They have nevertheless been recognized as paradigmatic examples of complex systems with applications to problems as diverse as neural networks, amorphous solids, biological molecules, social and economic interactions, information theory and constraint satisfaction problems.

This book presents an encyclopaedic overview of the broad range of these applications. More than 30 contributions are compiled, written by many of the leading researchers who have contributed to these developments over the last few decades. Some timely and cutting-edge applications are also discussed. This collection serves well as an introduction and summary of disordered and glassy systems for advanced undergraduates, graduate students and practitioners interested in the topic.

Contents:

• Simulated Annealing, Optimization, Searching for Ground States (Sergio Caracciolo, Alexander Hartmann, Scott Kirkpatrick and Martin Weigel)


• Beyond the Ising Spin Glass I: m-Vector, Potts, p-Spin, Spherical, Induced Moment, Random Graphs (David Sherrington and Jairo R L de Almeida)


• Beyond the Ising Spin Glass II: Spin Glass Without Replicas (J Michael Kosterlitz)


• Renormalization Group in Spin Glasses (Tom Lubensky, Tamás Temesvári, Imre Kondor and Maria Chiara Angelini)


• Numerical Simulations and Replica Symmetry Breaking (Víctor Martín-Mayor, Juan J Ruiz-Lorenzo, Beatriz Seoane and A Peter Young)


• The High-dimensional Landscape Paradigm: Spin-Glasses, and Beyond (Valentina Ros and Yan V Fyodorov)


• Universal Aspects of the Structural Glass Transition from Density Functional Theory (Theodore R Kirkpatrick and Dave Thirumalai)


• Non-Perturbative Processes in Glasses (Peter G Wolynes and Tommaso Rizzo)


• Dynamical Mean-Field Theory and the Aging Dynamics (Andrea Crisanti, Silvio Franz, Jorge Kurchan and Andrea Maiorano)


• Dynamical Heterogeneity in Glass-Forming Liquids (Giulio Biroli, Kunimasa Miyazaki and David R Reichman)


• The Kauzmann Transition to an Ideal Glass Phase (Chiara Cammarota, Misaki Ozawa and Gilles Tarjus)


• The Gardner Glass (Pierfrancesco Urbani, Yuliang Jin and Hajime Yoshino)


• The Jamming Transition and the Marginally Stable Solid (Francesco Arceri, Eric I Corwin and Corey S O’Hern)


• From Polymers to the KPZ Equation (Victor Dotsenko, Pierre Le Doussal and Henri Orland)


• Emergent Dynamics in Glasses and Disordered Systems: Correlations and Avalanches (Annette Zippelius, Matthias Fuchs, Alberto Rosso, James P Sethna and Matthieu Wyart)


• Replica Symmetry Breaking in Random Lasers: Experimental Measurement of the Overlap Distribution (Claudio Conti, Neda Ghofraniha, Luca Leuzzi and Giancarlo Ruocco)


• Anderson Localization on the Bethe Lattice (Saverio Pascazio, Antonello Scardicchio and Marco Tarzia)


• Quantum Glasses (Leticia F Cugliandolo and Markus Müller)


• The Cavity Method: From Exact Solutions to Algorithms (Alfredo Braunstein and Guilhem Semerjian)


• Message Passing and Its Applications (Florent Krzakala, Manfred Opper and David Saad)


• Information and Communication (Yoshiyuki Kabashima and Toshiyuki Tanaka)


• The Mighty Force: Statistical Inference and High-Dimensional Statistics (Erik Aurell, Jean Barbier, Aurélien Decelle and Roberto Mulet)


• Disordered Systems Insights on Computational Hardness (David Gamarnik, Cris Moore and Lenka Zdeborová)


• Neural Networks: From the Perceptron to Deep Nets (Marylou Gabrié, Surya Ganguli, Carlo Lucibello and Riccardo Zecchina)


• From the Statistical Physics of Disordered Systems to Neuroscience (Nicolas Brunel, Rémi Monasson, Haim Sompolinsky and J Leo van Hemmen)


• Statistical Physics of Biological Molecules (Simona Cocco, Andrea De Martino, Andrea Pagnani, Martin Weigt and Felix Ritort)


• Application of Spin Glass Ideas in Social Sciences, Economics and Finance (Jean-Philippe Bouchaud, Matteo Marsili and Jean-Pierre Nadal)


• Complex Dynamics in Ecological Systems and Animal Behavior (M Cristina Marchetti, Irene Giardina and A Altieri)


• Optimization of Random High-Dimensional Functions: Structure and Algorithms (Antonio Auffinger, Andrea Montanari and Eliran Subag)


• Rigorous Results in the Sherrington–Kirkpatrick Model (Wei-Kuo Chen, Dmitry Panchenko and Francesco Guerra)


• Random Energy Models: Broken Replica Symmetry and Activated Dynamics (Bernard Derrida, Peter Mottishaw and Véronique Gayrard)


• Rigorous Results: Random Constraint Satisfaction Problems (Amin Coja-Oghlan, Allan Sly and Nike Sun)


• Metastates and Replica Symmetry Breaking (C M Newman, N Read and D L Stein)


• Future Perspectives (Giorgio Parisi)

Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of statistical physics and its applications, with a particular focus on glassy and disordered systems, both classical and quantum, and computer science, ecological, biological and financial applications.

‘Several generations of scientists have been raised studying the book Spin glass theory and beyond published almost forty years ago, which presented what was then an emerging field full of promises. This volume now extends ‘far beyond’ these initial efforts, and provides an extensive account of the many solid branches that have grown out of the initial seeds. Many chapters cover directions that had not been anticipated, as new applications and extensions emerging from spin glass ideas are being developed by an ever growing community of researchers. This book summarizes an exciting scientific chapter in statistical mechanics and its modern applications.’ – Dr Ludovic Berthier Laboratoire Charles Coulomb Universite Montpellier & CNRS, France

‘The Parisi solution of the Spin Glass model, the Replica Symmetry Breaking, opened a new way to look at complexity in many different scientific fields from physics to biology, social sciences and optimisation procedures. This book aims at providing an in-depth and systematic review of the amazing results developed over the last few decades and it provides a source of inspiration to both young researchers approaching the field as well as to senior scientists challenging open questions and new possible insights.’ – Prof Roberto Benzi University of Rome Tor Vergata (Univ Roma ‘Tor Vergata’)Rome, Italy

‘Spin glass theory contains elegant mathematics, which induced the development of new groundbreaking concepts such as replica symmetry breaking, and unlocked the study of a myriad of other systems, from constraint satisfaction problems to ecosystems. This book succeeds in providing a much needed overview and description of the wide range of use of spin glass theory, reaching into disparate fields of application, and relying on contributions from top scientists in each subfield. Despite the broad scope of the book, it succeeds in presenting its content in a didactic way, and provides clear pointers for further study.’ – Marco BAITY JESIGroup leader SIAM Dept. Eawag (ETH), Switzerland

Key Features:

• An encyclopaedic overview of the physics of disordered and glassy systems, collecting methods and results obtained in forty years of intense research activity


• An introduction to the most timely and cutting-edge applications of the ideas stemming from the physics of disorder, from machine learning to ecology and finance


• A unique and outstanding collection of contributions from more than a hundred top-level researchers in the field, who introduce key concepts of their research