Spin Glasses
Last update: 25 Apr 2025 08:01First version: 6 May 2023
Yet Another Inadequate Placeholder
I am only being a little sarcastic when I say that a physicist interested in complex systems and trained in the 1990s (like me) was raised to look for spin glasses everywhere. There are times when I regard this as a childish thing I'm glad I put away, and times when it seems like a deep truth that the rest of the world would do well to appreciate...
- Recommended, big picture:
- K. H. Fischer and J. A. Hertz, Spin Glasses
- D. L. Stein, "Spin Glasses: Still Complex After All These Years?" cond-mat/0301104
- Daniel L. Stein and Charles M. Newman, Spin Glasses and Complexity
- Recommended, close-ups (very inadequate just now):
- Alia Abbara, Benjamin Aubin, Florent Krzakala, Lenka Zdeborová, "Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning", arxiv:1912.02729
- Giulio Biroli, Marc Mézard, "Kernel Density Estimators in Large Dimensions", arxiv:2408.05807 [comments]
- To read, over-views:
- Anton Bovier, Statistical Mechanics of Disordered Systems [enthusiastic review in J. Stat. Phys.]
- Tommaso Castellani and Andrea Cavagna, "Spin-Glass Theory for Pedestrians", cond-mat/0505032
- Viktor Dotsenko, Introduction to the Theory of Spin Glasses and Neural Networks
- Andrea Montanari and Subhabrata Sen, "A Short Tutorial on Mean-Field Spin Glass Techniques for Non-Physicists", arxiv:2204.02909 ["short" = 108 pages!]
- Michel Talagrand, Mean Field Models for Spin Glasses
- To read, making sense of the replica trick (which I have used, but don't grasp):
- Christopher L. Baldwin and Brian Swingle, "Revisiting the Replica Trick: Competition Between Spin Glass and Conventional Order", Journal of Statistical Physics 190 (2023): 125
- Viktor Dotsenko, Introduction to the Replica Theory of Disordered Statistical Systems
- To read, applications to optimization, neural networks, and computational complexity:
- M. Baity-Jesi, L. Sagun, M. Geiger, S. Spigler, G. Ben Arous, C. Cammarota, Y. LeCun, M. Wyart, G. Biroli, "Comparing Dynamics: Deep Neural Networks versus Glassy Systems", arxiv:1803.06969
- Nicholas P Baskerville, Jonathan P Keating, Francesco Mezzadri, Joseph Najnudel, "A spin-glass model for the loss surfaces of generative adversarial networks", arxiv:2101.02524
- Sourav Chatterjee, "Chaos, concentration, and multiple valleys", arxiv:0810.4221
- David Gamarnik, Cristopher Moore, Lenka Zdeborová, "Disordered Systems Insights on Computational Hardness", arxiv:2210.08312
- Levent Sagun, V. Ugur Guney, Gerard Ben Arous, Yann LeCun, "Explorations on high dimensional landscapes", arxiv:1412.6615
- To read, not otherwise or not yet classified:
- Elena Agliari, Raffaella Burioni, Pierluigi Contucci, "A Diffusive Strategic Dynamics for Social Systems", arxiv:0812.1435
- Jorge Fernandez-de-Cossio-Diaz, Roberto Mulet, "Spin Glass Theory of Interacting Metabolic Networks", arxiv:1909.11070
- Matthew Garrod, Nick S. Jones, "Influencing dynamics on social networks without knowledge of network microstructure", arxiv:2011.05774
- Steffen Lauritzen, Caroline Uhler, Piotr Zwiernik, "Total positivity in exponential families with application to binary variables", Annals of Statistics 49 (2021): 1436--1459
- Andrew Lucas, Ching Hua Lee, "Multistable binary decision making on networks", Physical Review E 87 (2013): 032806, arxiv:1210.6044
- Stein (ed.), Spin Glasses and Biology
- Shubham Tripathi, David A. Kessler, Herbert Levine, "Biological Regulatory Networks are Minimally Frustrated", Physical Review Letters 125 (2020): 088101, arxiv:1911.10252
- David Wales, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses
