Spin Glass Theory & Far Beyond

40 years of Replica Symmetry Breaking


The far-reaching implications of the theory of spin glasses were highlighted further by the 2021 Nobel Prize in Physics, of which half was awarded to Giorgio Parisi for “the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales.” Since the first observation in the 1960s, the theory of spin glasses has unexpectedly found applications in a wide array of scientific problems. This ranges from amorphous solids to movements of birds as they fly in a flock.

In Spin Glass Theory and Far Beyond, more than 30 contributions are compiled from more than 100 leading researchers who contributed to these applications over the last few decades. This volume provides a detailed introduction and review of spin glass research. While the fundamentals are expounded, cutting-edge and state-ofthe-art applications are also featured in this encyclopedic overview for enthusiastic readers in the 21st century

The volume is edited by Patrick Charbonneau, Enzo Marinari, Marc Mézard, Giorgio Parisi, Federico Ricci-Tersenghi, Gabriele Sicuro, and Francesco Zamponi.

Table of contents

  1. Sergio Caracciolo, Alexander K. Hartmann, Scott Kirkpatrick, Martin Weigel
    Simulated Annealing, Optimization, Searching for Ground States
  2. David Sherrington, Jairo R.L. de Almeida
    Beyond the Ising Spin Glass I: $m$-vector, Potts, $p$-spin, spherical, induced moment, random graphs
  3. Michael K. Kosterlitz
    Beyond the Ising Spin Glass II: Spin glass without replicas
  4. Renormalization Group in Spin Glasses
    1. Tom Lubenski
      Mean-Field and $\epsilon$-Expansion for Spin Glasses
    2. Tamás Temesvári, Imre Kondor
      Field theory for the de Almeida-Thouless transition
    3. Maria Chiara Angelini
      Real-space renormalization group for spin glasses
  5. Victor Martin-Mayor, Juan J. Ruiz-Lorenzo, Beatriz Seoane, A. Peter Young
    Numerical Simulations and Replica Symmetry Breaking
  6. Valentina Ros, Yan V. Fyodorov
    The High-Dimensional Landscapes Paradigm: Spin-Glasses, and Beyond
  7. Theodore R. Kirkpatrick, Dave Thirumalai
    Universal Aspects of the Structural Glass Transition from Density Functional Theory
  8. Non-Perturbative Processes in Glasses
    1. Peter Wolynes
      The Random First Order Transition Theory of Glasses in Real Space-Time: Instantons, Strings, Flames and Flows
    2. Tommaso Rizzo
      Stochastic equations and dynamics beyond mean-field theory
  9. Dynamical Mean-Field Theory and the Aging Dynamics
    1. Andrea Crisanti
      Equilibrium dynamics and Replica Symmetry Breaking in spin-glass systems
    2. Silvio Franz, Jorge Kurchan
      The relation between Parisi scheme and multi-thermalized dynamics in finite dimensions
    3. Andrea Maiorano
      Weak ergodicity breaking in mean-field spin glasses
  10. Giulio Biroli, Kunimasa Miyazaki, David R. Reichman
    Dynamical Heterogeneity in Glass-Forming Liquids
  11. Chiara Cammarota, Misaki Ozawa, Gilles Tarjus
    The Kauzmann Transition to an Ideal Glass Phase
  12. The Gardner Glass
    1. Pierfrancesco Urbani
      Low temperature amorphous solids: mean field theory and beyond
    2. Yuliang Jin, Hajime Yoshino
      Computer simulations of the Gardner transition in structural glasses
  13. Francesco Arceri, Eric I. Corwin, Corey S. O’Hern
    The Jamming Transition and the Marginally Stable Solid
  14. From Polymers to the KPZ Equation
    1. Victor Dotsenko, Pierre Le Doussal
      Directed polymers and the Kardar-Parisi-Zhang equation
    2. Henri Orland
      Heteropolymers and Proteins
  15. Emergent Dynamics in Glasses and Disordered Systems: Correlations and Avalanches
    1. Annette Zippelius, Matthias Fuchs
      From viscous fluids to elastic solids: A perspective on the glass transition
    2. Alberto Rosso, James P. Sethna, and Matthieu Wyart
      Avalanches and deformation in glasses and disordered systems
  16. Claudio Conti, Neda Ghofraniha, Luca Leuzzi, Giancarlo Ruocco
    Replica Symmetry Breaking in Random Lasers: Experimental Measurement of the Overlap Distribution
  17. Saverio Pascazio, Antonello Scardicchio, Marco Tarzia
    Anderson Localization on the Bethe Lattice
  18. Leticia Cugliandolo, Markus Müller
    Quantum Glasses ­— A review
  19. Alfredo Braunstein, Guilhem Semerjian
    The Cavity Method: From Exact Solutions to Algorithms
  20. Florent Krzakala, Manfred Opper, David Saad
    Message Passing and Its Applications
  21. Yoshiyuki Kabashima, Toshiyuki Tanaka
    Information and Communication
  22. Erik Aurell, Jean Barbier, Aurelien Decelle, Roberto Mulet
    The Mighty Force: Statistical Inference and High-Dimensional Statistics
  23. David Gamarnik, Cristopher Moore, Lenka Zdeborová
    Disordered Systems Insights on Computational Hardness
  24. Marylou Gabrié, Surya Ganguli, Carlo Lucibello, Riccardo Zecchina
    Neural Networks: From the Perceptron to Deep Nets
  25. From Statistical Physics of Disordered Systems to Neuroscience
    1. Nicolas Brunel, Rémi Monasson, Haim Sompolinsky
      Statistical Physics and Neuroscience
    2. J. Leo van Hemmen
      Neuronal Network and Spin Glass: A Non-Existing Relationship
  26. Statistical Physics of Biological Molecules
    1. Simona Cocco, Andrea De Martino, Andrea Pagnani, Martin Weigt
      Statistical-physics approaches to RNA molecules, families and networks
    2. Felix Ritort
      Molecular Replica Symmetry Breaking
  27. Jean-Philippe Bouchaud, Matteo Marsili, Jean-Pierre Nadal
    Application of Spin Glass Ideas in Social Sciences, Economics and Finance
  28. Complex Dynamics in Ecological Systems and Animal Behavior
    1. M. Cristina Marchetti
      Active Glasses and “Flying” Spin Glasses
    2. Irene Giardina
      Collective behavior in natural flocks: from data to models
    3. Ada Altieri
      Glassy features and complex dynamics in ecological systems
  29. Antonio Auffinger, Andrea Montanari, Eliran Subag
    Optimization of Random High-Dimensional Functions: Structure and Algorithms
  30. Rigorous Results in the Sherrington-Kirkpatrick Model
    1. Wei-Kuo Chen
      The Parisi formula
    2. Dmitry Panchenko
      Ultrametricity in spin glasses
    3. Francesco Guerra
      The replica trick in the frame of the interpolation perspective
  31. Random Energy Models: Broken Replica Symmetry and Activated Dynamics
    1. Bernard Derrida, Peter Mottishaw
      The Random Energy Models and Replica Symmetry Breaking
    2. Véronique Gayrard
      The Arcsine Law as a Universal Aging Scheme for Activated Dynamics of Random Energy Models
  32. Amin Coja-Oghlan, Allan Sly, Nike Sun
    Rigorous Results: Random Constraint Satisfaction Problems
  33. Charles M. Newman, Nicholas Read, Daniel L. Stein
    Metastates and Replica Symmetry Breaking
Gabriele Sicuro
Gabriele Sicuro
Formerly Lecturer in Disordered Systems, now Associate professor at University of Bologna