Introduction to the dynamics of disordered systems: Equilibrium and gradient descent

[en] This paper contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school Fundamental Problems in Statistical Physics XV, held in Brunico, Italy, in July 2021, and, just before that, at the summer school Glassy Systems and Inter-Disciplinary Applications, held in Cargese, France, in June 2021. The course was a short introductory overview of the dynamics of disordered systems, focused in particular on the equilibrium dynamics (with the associated glass transition), and on the simplest case of off-equilibrium dynamics, namely gradient descent. A few selected topics (and references) are chosen, based on the authors’ own taste and competences, and on pedagogical reasons, without aiming at a complete review of the subject.

Disciplines :

Physics

Author, co-author :

Folena, Giampaolo; Centre National de la Recherche Scientifique - CNRS > Laboratoire de Physique de l'École Normale Supérieure

MANACORDA, Alessandro ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

Zamponi, Francesco; Centre National de la Recherche Scientifique - CNRS > Laboratoire de Physique de l'École Normale Supérieure

External co-authors :

yes

Language :

English

Title :

Introduction to the dynamics of disordered systems: Equilibrium and gradient descent

Publication date :

01 December 2023

Journal title :

Physica A. Statistical Mechanics and its Applications

ISSN :

0378-4371

eISSN :

1873-2119

Publisher :

Elsevier, Amsterdam, Netherlands

Special issue title :

Lecture Notes of the 15th International Summer School of Fundamental Problems in Statistical Physics

Volume :

631

Pages :

128152

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Physics and Materials Science

European Projects :

H2020 - 723955 - GlassUniversality - Universal explanation of low-temperature glass anomalies

Funders :

CE - Commission Européenne
Union Européenne

Data Set :

https://doi.org/10.1016/j.physa.2022.128152

Available on ORBilu :

since 11 January 2023

Statistics

Number of views

71 (3 by Unilu)

Number of downloads

56 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

See more details

publications

supporting

mentioning

contrasting

Smart Citations

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography

Cavagna, A., Phys. Rep., 476, 2009, 51.
Sciortino, F., J. Stat. Mech. Theory Exp., 2005, 2005, P05015.
Castellani, T., Cavagna, A., J. Stat. Mech. Theory Exp., 2005, 2005, P05012.
Kirkpatrick, T.R., Thirumalai, D., J. Phys. A: Math. Gen., 22, 1989, L149.
O'Hern, C.S., Langer, S.A., Liu, A.J., Nagel, S.R., Phys. Rev. Lett., 88, 2002, 075507.
O'Hern, C.S., Silbert, L.E., Liu, A.J., Nagel, S.R., Phys. Rev. E, 68, 2003, 011306.
Liu, A.J., Nagel, S.R., Annu. Rev. Condens. Matter Phys., 1, 2010, 347.
Liu, A., Nagel, S., Van Saarloos, W., Wyart, M., Berthier, L., Biroli, G., Bouchaud, J.-P., Cipelletti, L., van Saarloos, W., (eds.) Dynamical Heterogeneities and Glasses, 2011, Oxford University Press arXiv:1006.2365.
Conway, J.H., Sloane, N.J.A., Sphere Packings, Lattices and Groups. 1993, Spriger-Verlag.
Torquato, S., Stillinger, F.H., Rev. Modern Phys., 82, 2010, 2633.
MacWilliams, F.J., Sloane, N.J.A., The Theory of Error Correcting Codes, Vol. 16. 1977, Elsevier.
Huffman, W.C., Pless, V., Fundamentals of Error-Correcting Codes. 2010, Cambridge University Press.
Altarelli, F., Monasson, R., Semerjian, G., Zamponi, F., Biere, A., Heule, M., van Maaren, H., Walsh, T., (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, 2009, IOS Press arXiv:0802.1829.
Franz, S., Parisi, G., J. Phys. A, 49, 2016, 145001.
Applegate, D.L., Bixby, R.E., Chvataĺ, V., Cook, W.J., The Traveling Salesman Problem: A Computational Study. 2011, Princeton University Press.
Several practical applications of the TSP and an interactive visualization for learning/teaching the problem can be found at http://www.math.uwaterloo.ca/tsp/index.html.
Jensen, T.R., Toft, B., Graph Coloring Problems. 2011, John Wiley & Sons.
Cheeseman, P.C., Kanefsky, B., Taylor, W.M., IJCAI, Vol. 91. 1991, 331–337.
Mitchell, D., Selman, B., Levesque, H., AAAI, Vol. 92. 1992, Citeseer, 459–465.
Kirkpatrick, S., Selman, B., Science, 264, 1994, 1297.
Selman, B., Kirkpatrick, S., Artificial Intelligence, 81, 1996, 273.
Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B., Troyansky, L., Nature, 400, 1999, 133.
Engel, A., Van den Broeck, C., Statistical Mechanics of Learning. 2001, Cambridge University Press.
Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L., Rev. Modern Phys., 91, 2019, 045002.
Gardner, E., Europhys. Lett., 4, 1987, 481.
M. Geiger, L. Petrini, M. Wyart, arXiv:2012.15110, 2020.
D'Ascoli, Stéphane, Refinetti, Maria, Biroli, Giulio, Krzakala, Florent, Double trouble in double descent: bias and variance(s) in the lazy regime. Proceedings of the 37th International Conference on Machine Learning III, Hal Daumé, Singh, Aarti, (eds.) Proceedings of Machine Learning Research, 2020, PMLR, 2280–2290.
Mignacco, F., Krzakala, F., Urbani, P., Zdeborová, L., J. Stat. Mech. Theory Exp., 2021, 2021, 124008.
F. Mignacco, P. Urbani, arXiv:2112.10852, 2021.
Schneidman, E., Berry, M.J., Segev, R., Bialek, W., Nature, 440, 2006, 1007.
Cocco, S., Leibler, S., Monasson, R., Proc. Natl. Acad. Sci., 106, 2009, 14058.
Morcos, F., Pagnani, A., Lunt, B., Bertolino, A., Marks, D.S., Sander, C., Zecchina, R., Onuchic, J.N., Hwa, T., Weigt, M., Proc. Natl. Acad. Sci., 108, 2011, E1293.
Zdeborová, L., Krzakala, F., Adv. Phys., 65, 2016, 453.
Cocco, S., Feinauer, C., Figliuzzi, M., Monasson, R., Weigt, M., Rep. Progr. Phys., 81, 2018, 032601.
Ros, V., Arous, G.B., Biroli, G., Cammarota, C., Phys. Rev. X, 9, 2019, 011003.
Mannelli, Stefano Sarao, Krzakala, Florent, Urbani, Pierfrancesco, Zdeborova, Lenka, Passed & spurious: descent algorithms and local minima in spiked matrix-tensor models. Proceedings of the 36th International Conference on Machine Learning Chaudhuri, Kamalika, Salakhutdinov, Ruslan, (eds.) Proceedings of Machine Learning Research, 2019, PMLR, 4333–4342.
Mannelli, S.S., Biroli, G., Cammarota, C., Krzakala, F., Urbani, P., Zdeborová, L., Phys. Rev. X, 10, 2020, 011057.
Mignacco, F., Urbani, P., Zdeborová, L., Mach. Learn.: Sci. Technol., 2, 2021, 035029.
Antenucci, F., Franz, S., Urbani, P., Zdeborová, L., Phys. Rev. X, 9, 2019, 011020.
Trinquier, J., Uguzzoni, G., Pagnani, A., Zamponi, F., Weigt, M., Nature Commun., 12, 2021, 1.
Cocco, S., Monasson, R., Posani, L., Rosay, S., Tubiana, J., Physica A, 504, 2018, 45.
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., Science, 220, 1983, 671.
Cugliandolo, L.F., Kurchan, J., Phys. Rev. Lett., 71, 1993, 173.
Montanari, A., Ricci-Tersenghi, F., Phys. Rev. B, 70, 2004, 134406.
Zdeborová, L., Krzakala, F., Phys. Rev. B, 81, 2010, 224205.
Krzakala, F., Zdeborová, L., J. Phys. Conf. Ser., 473, 2013, 12022.
Folena, G., Franz, S., Ricci-Tersenghi, F., Phys. Rev. X, 10, 2020, 031045.
Cugliandolo, L., Barrat, J., Feigelman, M., Kurchan, J., Dalibard, J., (eds.) Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, 2003, Springer-Verlag arXiv:cond-mat/0210312.
J. Kurchan, arXiv:0901.1271, 2009.
Kirkpatrick, T.R., Wolynes, P.G., Phys. Rev. A, 35, 1987, 3072.
Kirkpatrick, T.R., Thirumalai, D., Phys. Rev. Lett., 58, 1987, 2091.
Kirkpatrick, T.R., Thirumalai, D., Phys. Rev. B, 36, 1987, 5388.
Kirkpatrick, T.R., Wolynes, P.G., Phys. Rev. B, 36, 1987, 8552.
Derrida, B., Phys. Rev. B, 24, 1981, 2613.
Gross, D.J., Mézard, M., Nuclear Phys. B, 240, 1984, 431.
Gross, D., Kanter, I., Sompolinsky, H., Phys. Rev. Lett., 55, 1985, 304.
Gardner, E., Nuclear Phys. B, 257, 1985, 747.
Kirkpatrick, T.R., Thirumalai, D., Wolynes, P.G., Phys. Rev. A, 40, 1989, 1045.
Crisanti, A., Sommers, H.-J., Z. Phys. B Condensed Matter, 87, 1992, 341.
Crisanti, A., Horner, H., Sommers, H.-J., Z. Phys. B Condensed Matter, 92, 1993, 257.
Folena, G., The mixed p-spin model: selecting, following and losing states. 2020 https://tel.archives-ouvertes.fr/tel-02883385.
Sompolinsky, H., Zippelius, A., Phys. Rev. Lett., 47, 1981, 359.
Sompolinsky, H., Zippelius, A., Phys. Rev. B, 25, 1982, 6860.
Franz, S., Tria, F., J. Stat. Phys., 122, 2006, 313.
Auffinger, A., Arous, G.B., Ann. Probab., 41, 2013, 4214.
Auffinger, A., Arous, G.B., Cernỳ̌, J., Comm. Pure Appl. Math., 66, 2013, 165.
Subag, E., Invent. Math., 210, 2017, 135.
Auffinger, A., Chen, W.-K., Adv. Math., 330, 2018, 553.
Arous, G.B., Subag, E., Zeitouni, O., Comm. Pure Appl. Math., 73, 2020, 1732.
Kosterlitz, J.M., Thouless, D.J., Jones, R.C., Phys. Rev. Lett., 36, 1976, 1217.
Barbier, D., Cugliandolo, L.F., Lozano, G.S., Nessi, N., Europhys. Lett., 132, 2020, 50002.
Mézard, M., Parisi, G., Virasoro, M.A., Spin Glass Theory and beyond. 1987, World Scientific.
Sastry, S., Debenedetti, P.G., Stillinger, F.H., Nature, 393, 1998, 554.
Franz, S., Parisi, G., J. Physique I, 5, 1995, 1401.
Monasson, R., Phys. Rev. Lett., 75, 1995, 2847.
Götze, W., Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory, Vol. 143. 2008, OUP Oxford.
Kurchan, J., Parisi, G., Virasoro, M.A., J. Physique I, 3, 1993, 1819.
Crisanti, A., Sommers, H.-J., J. Physique I, 5, 1995, 805.
Folena, G., Franz, S., Ricci-Tersenghi, F., J. Stat. Mech. Theory Exp., 2021, 2021, 033302.
Barrat, A., Franz, S., Parisi, G., J. Phys. A: Math. Gen., 30, 1997, 5593.
Barrat, A., Burioni, R., Mézard, M., J. Phys. A: Math. Gen., 29, 1996, L81.
Cavagna, A., Giardina, I., Parisi, G., Phys. Rev. B, 57, 1998, 11251.
Sun, Y., Crisanti, A., Krzakala, F., Leuzzi, L., Zdeborová, L., J. Stat. Mech. Theory Exp., 2012, 2012, P07002.
Bouchaud, J.-P., J. Physique I, 2, 1992, 1705.
Bouchaud, J., Cugliandolo, L., Kurchan, J., Mezard, M., Young, A., (eds.) Spin Glasses and Random Fields, 1998, World Scientific Pub Co Inc arXiv.org:cond-mat/9702070.
Franz, S., Marinari, E., Parisi, G., J. Phys. A: Math. Gen., 28, 1995, 5437.
Ozawa, M., Kuroiwa, T., Ikeda, A., Miyazaki, K., Phys. Rev. Lett., 109, 2012, 205701.
Charbonneau, P., Morse, P.K., Phys. Rev. Lett., 126, 2021, 088001.
Montanari, A., Semerjian, G., J. Stat. Phys., 125, 2006, 23.
Rosenblatt, F., Psychol. Rev., 65, 1958, 386.
Block, H.-D., Rev. Modern Phys., 34, 1962, 123.
Gardner, E., Derrida, B., J. Phys. A: Math. Gen., 21, 1988, 271.
Abbaras, Alia, Aubin, Benjamin, Krzakala, Florent, Zdeborová, Lenka, Rademacher complexity and spin glasses: a link between the replica and statistical theories of learning. Proceedings of The First Mathematical and Scientific Machine Learning Conference Lu, Jianfeng, Ward, Rachel, (eds.) Proceedings of Machine Learning Research, 2020, PMLR, 27–54.
Franz, S., Parisi, G., Sevelev, M., Urbani, P., Zamponi, F., Sevelev, M., SciPost Phys., 2, 2017, 019.
Hwang, S., Ikeda, H., Phys. Rev. E, 101, 2020, 052308.
Mézard, M., J. Phys. A: Math. Gen., 22, 1989, 2181.
Altieri, A., Franz, S., Parisi, G., J. Stat. Mech. Theory Exp., 2016, 2016, 093301.
Altieri, A., Phys. Rev. E, 97, 2018, 012103.
Agoritsas, E., Biroli, G., Urbani, P., Zamponi, F., J. Phys. A, 51, 2018, 085002.
Manacorda, A., Zamponi, F., J. Phys. A, 55, 2022, 334001.
Maimbourg, T., Kurchan, J., Zamponi, F., Phys. Rev. Lett., 116, 2016, 015902.
Franz, S., Parisi, G., Urbani, P., Zamponi, F., Proc. Natl. Acad. Sci., 112, 2015, 14539.
Wyart, M., Nagel, S., Witten, T., Europhys. Lett., 72, 2005, 486.
DeGiuli, E., Laversanne-Finot, A., Düring, G., Lerner, E., Wyart, M., Soft Matter, 10, 2014, 5628.
Sclocchi, A., Urbani, P., Phys. Rev. E, 105, 2022, 024134.
Lerner, E., Düring, G., Wyart, M., Europhys. Lett., 99, 2012, 58003.
Ikeda, A., Kawasaki, T., Berthier, L., Saitoh, K., Hatano, T., Phys. Rev. Lett., 124, 2020, 058001.
Ikeda, H., J. Chem. Phys., 153, 2020, 126102.
Nishikawa, Y., Ikeda, A., Berthier, L., J. Stat. Phys., 182, 2021, 1.
Chacko, R.N., Sollich, P., Fielding, S.M., Phys. Rev. Lett., 123, 2019, 108001.
Nishikawa, Y., Ozawa, M., Ikeda, A., Chaudhuri, P., Berthier, L., Phys. Rev. X, 12, 2022, 021001.
Wyart, M., Phys. Rev. Lett., 109, 2012, 125502.
Charbonneau, P., Kurchan, J., Parisi, G., Urbani, P., Zamponi, F., Nature Commun., 5, 2014, 3725.
Charbonneau, P., Corwin, E.I., Parisi, G., Zamponi, F., Phys. Rev. Lett., 114, 2015, 125504.
Kallus, Y., Phys. Rev. E, 93, 2016, 012902.
Charbonneau, P., Kurchan, J., Parisi, G., Urbani, P., Zamponi, F., Annu. Rev. Condens. Matter Phys., 8, 2017, 265.
Franz, S., Sclocchi, A., Urbani, P., Phys. Rev. Lett., 123, 2019, 115702.
Franz, S., Sclocchi, A., Urbani, P., SciPost Phys., 9, 2020, 012.
Charbonneau, P., Corwin, E.I., Dennis, R.C., Rojas, R.D.H., Ikeda, H., Parisi, G., Ricci-Tersenghi, F., Phys. Rev. E, 104, 2021, 014102.
DeGiuli, E., Lerner, E., Brito, C., Wyart, M., Proc. Natl. Acad. Sci., 111, 2014, 17054.
Müller, M., Wyart, M., Ann. Rev. Cond. Mat., 6, 2015, 177.
Biroli, G., Charbonneau, P., Hu, Y., Ikeda, H., Szamel, G., Zamponi, F., J. Phys. Chem. B, 125, 2021, 6244.
Ikeda, H., Urbani, P., Zamponi, F., J. Phys. A, 52, 2019, 344001.
Brito, C., Ikeda, H., Urbani, P., Wyart, M., Zamponi, F., Proc. Natl. Acad. Sci., 115, 2018, 11736.
Franz, S., Sclocchi, A., Urbani, P., J. Stat. Mech. Theory Exp., 2021, 2021, 023208.