Rev. Mod. Phys. 95, 030501 – Published 17 August, 2023
DOI: https://doi.org/10.1103/RevModPhys.95.030501
Abstract
This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this concept in the framework of statistical mechanics. Finally, I will briefly mention the cornucopia of applications of these ideas both in physics and in other disciplines.
Physics Subject Headings (PhySH)
- *The 2021 Nobel Prize for Physics was shared by Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi. This paper is the text of the address given in conjunction with the award.
Article Text
References (189)
- Aizenman, M., and P. Contucci, 1998, J. Stat. Phys. 92, 765.
- Aizenman, M., R. Sims, and S. L. Starr, 2003, Phys. Rev. B 68, 214403.
- Albert, S., Th. Bauer, M. Michl, G. Biroli, J.-P. Bouchaud, A. Loidl, P. Lunkenheimer, R. Tourbot, C. Wiertel-Gasquet, and F. Ladieu, 2016, Science 352, 1308.
- Altieri, A., F. Roy, C. Cammarota, and G. Biroli, 2021, Phys. Rev. Lett. 126, 258301.
- Amit, D., 1989, Modeling Brain Function: The World of Attractor Neural Networks (Cambridge University Press, Cambridge, England).
- Amit, D. J., H. Gutfreund, and H. Sompolinsky, 1985a, Phys. Rev. A 32, 1007.
- Amit, D. J., H. Gutfreund, and H. Sompolinsky, 1985b, Phys. Rev. Lett. 55, 1530.
- Anderson, P. W., 1979, in Ill-Condensed Matter, Proceedings of the Les Houches Summer School, Session XXXI, edited by R. Balian, R. Maynard, and G. Toulouse (North-Holland, Amsterdam).
- Anderson, P. W, 1989, “Spin glasses VI: Spin glasses as cornucopia,” Phys. Today 42, No. 9, 9.
- Angelani, L., C. Conti, G. Ruocco, and F. Zamponi, 2006, Phys. Rev. Lett. 96, 065702.
- Angelini, M. C., C. Lucibello, G. Parisi, G. Perrupato, F. Ricci-Tersenghi, and T. Rizzo, 2022, Phys. Rev. Lett. 128, 075702.
- Aspelmeier, T., A. Billoire, E. Marinari, and M. A. Moore, 2008, J. Phys. A 41, 324008.
- Baity-Jesi, M., et al. (Janus Collaboration), 2017a, Phys. Rev. Lett. 118, 157202.
- Baity-Jesi, M., et al. (Janus Collaboration), 2017b, Proc. Natl. Acad. Sci. U.S.A. 114, 1838.
- Baity-Jesi, M., et al. (Janus Collaboration), 2018, Phys. Rev. Lett. 120, 267203.
- Baity-Jesi, M., et al. (Janus Collaboration), 2021, Commun. Phys. 4, 74.
- Baity-Jesi, M., et al. (Janus Collaboration), 2022, arXiv:2207.06207.
- Banos, R. A., et al. (Janus Collaboration), 2010a, Phys. Rev. Lett. 105, 177202.
- Banos, R. A., et al. (Janus Collaboration), 2010b, J. Stat. Mech. P06026.
- Banos, R. A., et al. (Janus Collaboration), 2011, Phys. Rev. B 84, 174209.
- Barrat, A., S. Franz, and G. Parisi, 1997, J. Phys. A 30, 5593.
- Behringer, R. P., and B. Chakraborty, 2019, Rep. Prog. Phys. 82, 012601.
- Berthier, L., P. Charbonneau, Y. Jin, G. Parisi, B. Seoane, and F. Zamponi, 2016, Proc. Natl. Acad. Sci. U.S.A. 113, 8397.
- Billoire, A., L. A. Fernandez, A. Maiorano, E. Marinari, V. Martin-Mayor, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenz, and D. Yllanes, 2013, Phys. Rev. Lett. 110, 219701.
- Billoire, A., A. Maiorano, E. Marinari, V. Martin-Mayor, and D. Yllanes, 2014, Phys. Rev. B 90, 094201.
- Billoire, A., L. A. Fernandez, A. Maiorano, E. Marinari, V. Martin-Mayor, J. Moreno-Gordo, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, 2018, J. Stat. Mech. 033302.
- Binder, K., and A. P. Young, 1986, Rev. Mod. Phys. 58, 801.
- Biroli, G., G. Bunin, and C. Cammarota, 2018, New J. Phys. 20, 083051.
- Biscari, P., and G. Parisi, 1995, J. Phys. A 28, 4697.
- Blandin, A., 1978, J. Phys. Colloq. 39, C6-1516, https://hal.science/jpa-00218086/document.
- Boettcher, S., 2005, Phys. Rev. Lett. 95, 197205.
- Bollini, C. G., and J. J. Giambiagi, 1972, Phys. Lett. 40B, 566.
- Bouchaud, J. P., and G. Biroli, 2004, J. Chem. Phys. 121, 7347.
- Bray, A. J., and M. A. Moore, 1978, Phys. Rev. Lett. 41, 1068.
- Bray, A. J., and M. A. Moore, 1980, J. Phys. C 13, L469.
- Bray, A. J., and S. A. Roberts, 1980, J. Phys. C 13, 5405.
- Brout, R., 1959, Phys. Rev. 115, 824.
- Campellone, M., G. Parisi, and M. A. Virasoro, 2010, J. Stat. Phys. 138, 29.
- Cannella, V., J. A. Mydosh, and J. I. Budnick, 1971, J. Appl. Phys. 42, 1689.
- Cavagna, A., 2009, Phys. Rep., 476, 51.
- Cavagna, A., I. Giardina, and G. Parisi, 1997a, J. Phys. A 30, 7021.
- Cavagna, A., I. Giardina, and G. Parisi, 1997b, arXiv:cond-mat/9702069.
- Cavagna, A., I. Giardina, and G. Parisi, 1998, Phys. Rev. B 57, 11251.
- Cavagna, A., I. Giardina, and G. Parisi, 1999, Phys. Rev. Lett. 83, 108.
- Charbonneau, P., 2022, arXiv:2211.01802.
- Charbonneau, P., E. I. Corwin, R. C. Dennis, R. D. H. Rojas, H. Ikeda, G. Parisi, and F. Ricci-Tersenghi, 2021, Phys. Rev. E 104, 014102.
- Charbonneau, P., J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, 2014a, Nat. Commun. 5, 3725.
- Charbonneau, P., J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, 2014b, J. Stat. Mech. P10009.
- Charbonneau, P., J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, 2017, Annu. Rev. Condens. Matter Phys. 8, 265.
- Charbonneau, P., M. Mézard, E. Marinari, F. Ricci-Tersenghi, G. Sicuro, and F. Zamponi, 2023, Eds., Spin Glass Theory and Far Beyond—Replica Symmetry Breaking after 40 Years (World Scientific, Singapore).
- Charbonneau, P., and F. Zamponi, 2022, https://caphes.ens.fr/history-of-replica-symmetry-breaking-in-physics/.
- Coluzzi, B., M. Mézard, G. Parisi, and P. Verrocchio, 1999, J. Chem. Phys. 111, 9039.
- Cugliandolo, L. F., and J. Kurchan, 1993, Phys. Rev. Lett. 71, 173.
- Cugliandolo, L. F., and J. Kurchan1994, J. Phys. A 27, 5749.
- Cugliandolo, L. F., J. Kurchan, and L. Peliti, 1997, Phys. Rev. E 55, 3898.
- de Almeida, J. R. L., and D. J. Thouless, 1978, J. Phys. A 11, 983.
- Debreu, G., 1970, Econometrica 38, 387.
- De Dominicis, C., M. Gabay, T. Garel, and H. Orland, 1980, J. Phys. (Paris) 41, 923.
- De Dominicis, C., and T. Garel, 1979, J. Phys. Lett. 40, 575.
- De Dominicis, C., and I. Kondor, 1983, Phys. Rev. B 27, 606.
- De Dominicis, C., and I. Kondor, 1984, J. Phys. Lett. 45, 205.
- De Dominicis, C., T. Temesvari, and I. Kondor, 1998, J. Phys. IV (France) 08, Pr6-13.
- De Dominicis, C., and A. P. Young, 1983, J. Phys. A 16, 2063.
- de Gennes, P. G., 1972, Phys. Lett. 38A, 339.
- Derrida, B., 1981, Phys. Rev. B 24, 2613.
- Derrida, B., 1985, J. Phys. Lett. 46, 401.
- Djurberg, C., K. Jonason, and P. Nordblad, 1999, Eur. Phys. J. B 10, 15.
- Drouffe, J.-M., G. Parisi, and N. Sourlas, 1979, Nucl. Phys. B161, 397.
- Edwards, S. F., and P. W. Anderson, 1975, J. Phys. F 5, 965.
- Efetov, K. B., 1983, Adv. Phys. 32, 53.
- Eldredge, N., and S. J. Gould, 1972, in Models in Paleobiology, edited by Thomas J. M. Schopf (Freeman, Cooper, San Francisco), pp. 82–115.
- Fortuin, C. M., and P. W. Kasteleyn, 1972, Physica (Amsterdam) 57, 536.
- Franz, S., S. Hwang, and P. Urbani, 2019, Phys. Rev. Lett. 123, 160602.
- Franz, S., and J. Kurchan, 2023, in Spin Glass Theory and Far Beyond—Replica Symmetry Breaking after 40 Years, edited by P. Charbonneau, M. Mezard, E. Marinari, F. Ricci-Tersenghi, G. Sicuro, and F. Zamponi (World Scientific, Singapore).
- Franz, S., M. Mézard, G. Parisi, and L. Peliti, 1998, Phys. Rev. Lett. 81, 1758.
- Franz, S., M. Mézard, G. Parisi, and L. Peliti1999, J. Stat. Phys. 97, 459.
- Franz, S., and G. Parisi, 1995, J. Phys. I (France) 5, 1401.
- Franz, S., and G. Parisi, 1998, arXiv:cond-mat/9804084.
- Franz, S., and G. Parisi, 2013, J. Stat. Mech. P02003.
- Franz, S., G. Parisi, F. Ricci-Tersenghi, and T. Rizzo, 2011, Eur. Phys. J. E, 34, 1.
- Franz, S., G. Parisi, and M. A. Virasoro, 1994, J. Phys. I (France) 4, 1657.
- Franz, S., and M. A. Virasoro, 2000, J. Phys. A 33, 891.
- Gardner, E., 1985, Nucl. Phys., B257, 747.
- Gardner, E., 1987, Europhys. Lett. 4, 481.
- Gardner, E., and B. Derrida, 1988, J. Phys. A 21, 271.
- Ghirlanda, S., and F. Guerra, 1998, J. Phys. A 31, 9149.
- Ghofraniha, N., I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, 2015, Nat. Commun. 6, 6058.
- Goldstein, M., 1969, J. Chem. Phys. 51, 3728.
- Gomes, A., E. P. Raposo, A. L. Moura, S. I. Fewo, P. I. R. Pincheira, V. Jerez, L. J. Q. Maia, and C. B. de Araújo, 2016, Sci. Rep. 6, 27987.
- Gomes, Anderson S. L., Bismarck C. Lima, Pablo I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, 2016, Phys. Rev. A 94, 011801.
- Gomes, Anderson S. L., André L. Moura, Cid B. de Araújo, and Ernesto P. Raposo, 2021, Prog. Quantum Electron. 78, 100343.
- Götze, W., 2009, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford University Press, New York).
- Gross, D. J., I. Kanter, and H. Sompolinsky, 1985, Phys. Rev. Lett. 55, 304.
- Guerra, F., 2003, Commun. Math. Phys. 233, 1.
- Guerra, F., and F. L. Toninelli, 2002, Commun. Math. Phys. 230, 71.
- Hammond, A. P., and E. I. Corwin, 2020, Proc. Natl. Acad. Sci. U.S.A. 117, 5714.
- Hebb, D. O., 1949, The Organization of Behavior (Wiley, New York).
- Hérisson, D., and M. Ocio, 2002, Phys. Rev. Lett. 88, 257202.
- ’t Hooft, G., and M. Veltman, 1972, Nucl. Phys. B44, 189.
- Hopfield, J. J., 1982, Proc. Natl. Acad. Sci. U.S.A. 79, 2554.
- Hukushima, K., and K. Nemoto, 1996, J. Phys. Soc. Jpn., 65, 1604.
- Joh, Y. G., R. Orbach, G. G. Wood, J. Hammann, and E. Vincent, 1999, Phys. Rev. Lett. 82, 438.
- Joh, Y. G., R. Orbach, G. G. Wood, J. Hammann, and E. Vincent, 2000, J. Phys. Soc. Jpn. 69, 215 [arXiv:cond-mat/0002040].
- Jonason, K., E. Vincent, J. Hammann, J. P. Bouchaud, and P. Nordblad, 1998, Phys. Rev. Lett. 81, 3243.
- Kabashima, Y., F. Krzakala, M. Mézard, A. Sakata, and L. Zdeborová, 2016, IEEE Trans. Inf. Theory 62, 4228.
- Kirkpatrick, S., C. D. Gelatt, Jr., and M. P. Vecchi, 1983, Science 220, 671.
- Kirkpatrick, T. R., and D. Thirumalai, 1987a, Phys. Rev. Lett. 58, 2091.
- Kirkpatrick, T. R., and D. Thirumalai1987b, Phys. Rev. B 36, 5388.
- Kirkpatrick, T. R., D. Thirumalai, and P. G. Wolynes, 1989, Phys. Rev. A 40, 1045.
- Kirkpatrick, T. R., D. Thirumalai, and P. G. Wolynes, 2022, Proc. Natl. Acad. Sci. U.S.A., 119, e2204879119.
- Kirkpatrick, T. R., and P. G. Wolynes, 1987, Phys. Rev. A 35, 3072.
- Kondor, I., 2021, Fiz. Sz. LXXI, 365, http://www.fizikaiszemle.hu.
- Krauth, W., and M. Mézard, 1989, J. Phys. (Paris) 50, 3057.
- Krzakala, F., M. Mézard, F. Sausset, Y. F. Sun, and L. Zdeborová, 2012, Phys. Rev. X 2, 021005.
- Kurchan, J., G. Parisi, P. Urbani, and F. Zamponi, 2013, J. Phys. Chem. B 117, 12979.
- Kurchan, J., G. Parisi, and F. Zamponi, 2012, J. Stat. Mech. P10012.
- Lerner, E., and M. Wyart, 2014, Soft Matter 10, 5628.
- Liao, Q., and L. Berthier, 2019, Phys. Rev. X 9, 011049.
- Little, W. A., 1974, Math. Biosci. 19, 101.
- Liu, A. J., and S. R. Nagel, 2010, Annu. Rev. Condens. Matter Phys. 1, 347.
- Lubensky, T. C., and J. Isaacson, 1978, Phys. Rev. Lett. 41, 829.
- Lucibello, C., G. Parisi, and G. Sicuro, 2017, Phys. Rev. E 95, 012302.
- Maiorano, A., and G. Parisi, 2018, Proc. Natl. Acad. Sci. U.S.A. 115, 5129.
- Maiorano, A., G. Parisi, and D. Yllanes, 2013, arXiv:1312.2790.
- Marinari, E., and G. Parisi, 1992, Europhys. Lett. 19, 451.
- Marinari, E., G. Parisi, F. Ricci-Tersenghi, J. Ruiz-Lorenzo, and F. Zuliani, 2000, J. Stat. Phys. 98, 973.
- Marinari, E., G. Parisi, and F. Ritort, 1994a, J. Phys. A 27, 7615.
- Marinari, E., G. Parisi, and F. Ritort, 1994b, J. Phys. A27, 7647.
- Marino, R., G. Parisi, and F. Ricci-Tersenghi, 2016, Nat. Commun. 7, 12996.
- Massaro, L. M., S. Gentilini, A. Portone, A. Camposeo, D. Pisignano, C. Conti, and N. Ghofraniha, 2021, ACS Photonics 8, 376.
- Mattia, M., and P. Del Giudice, 2002, Phys. Rev. E 66, 051917.
- May, R., 1972, Nature (London) 238, 413.
- Mezard, M., and G. J. Parisi, 1991, J. Phys. I (France) 1, 809, https://hal.science/file/index/docid/246372/filename/ajp-jp1v1p809.pdf.
- Mézard, M., and G. Parisi, 1987, J. Phys. (Paris) 48, 1451.
- Mézard, M., and G. Parisi, 1999, J. Chem. Phys. 111, 1076.
- Mézard, M., and G. Parisi, 2001, Eur. Phys. J. B 20, 217.
- Mézard, M., and G. Parisi, 2003, J. Stat. Phys. 111, 1.
- Mézard, M., G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, 1984a, Phys. Rev. Lett. 52, 1156.
- Mézard, M., G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, 1984b, J. Phys. (Paris) 45, 843, https://hal.science/jpa-00209816/file/ajp-jphys_1984_45_5_843_0.pdf.
- Mézard, M., G. Parisi, and M. A. Virasoro, 1985, J. Phys. Lett. 46, 217.
- Mézard, M., G. Parisi, and M. A. Virasoro, 1987, Spin Glass Theory and Beyond (World Scientific, Singapore).
- Mézard, M., G. Parisi, and R. Zecchina, 2002, Science 297, 812.
- Monasson, R., and R. Zecchina, 1996, Phys. Rev. Lett. 76, 3881.
- Monasson, R., R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, 1999, Nature (London) 400, 133.
- Montanari, A., and F. Ricci-Tersenghi, 2003, Eur. Phys. J. B 33, 339.
- Mulet, R., A. Pagnani, M. Weigt, and R. Zecchina, 2002, Phys. Rev. Lett. 89, 268701.
- Onuchic, J. N., and P. G. Wolynes, 2004, Curr. Opin. Struct. Biol. 14, 70.
- Pagnani, A., G. Parisi, and F. Ricci-Tersenghi, 2000, Phys. Rev. Lett. 84, 2026.
- Panchenko, D., 2012, J. Stat. Phys. 149, 362.
- Panchenko, D., 2013a, Ann. Math. 177, 383.
- Panchenko, D., 2013b, The Sherrington-Kirkpatrick Model (Springer Science, Berlin).
- Parisi, G., 1979a, Phys. Lett. 73A, 203.
- Parisi, G., 1979b, Phys. Rev. Lett. 43, 1754.
- Parisi, G., 1980, J. Phys. A 13, L115.
- Parisi, G., 1981, J. Phys. A 14, 735.
- Parisi, G., 1983, Phys. Rev. Lett. 50, 1946.
- Parisi, G., 1984, in Recent Advances in Field Theory and Statistical Mechanics, Proceedings of the Les Houches Summer School, Session XXXIX, edited by J. B. Zuber and R. Stora (North-Holland, Amsterdam).
- Parisi, G., 1988, Statistical Field Theory (Addison-Wesley, Reading, MA).
- Parisi, G., 1992, Field Theory, Disorder and Simulations (World Scientific, Singapore).
- Parisi, G., 2003, Bull. Symb. Log. 9, 181.
- Parisi, G., 2017, J. Stat. Phys. 167, 515.
- Parisi, G., 2023a, in Spin Glass Theory and Far Beyond—Replica Symmetry Breaking after 40 Years, edited by P. Charbonneau, M. Mezard, E. Marinari, F. Ricci-Tersenghi, G. Sicuro, and F. Zamponi (World Scientific, Singapore).
- Parisi, G., 2023b, In a Flight of Starlings: How Nature Unlocks the Wonders of Physics (Penguin Press, Toronto).
- Parisi, G., P. Ranieri, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, 1997, J. Phys. A 30, 7115.
- Parisi, G., and M. Ratiéville, 2002, Eur. Phys. J. B 29, 457.
- Parisi, G., F. Ricci-Tersenghi, and D. Yllanes, 2015, J. Stat. Mech. P05002.
- Parisi, G., and N. Sourlas, 1979, Phys. Rev. Lett. 43, 744.
- Parisi, G., P. Urbani, and F. Zamponi, 2020, Theory of Simple Glasses: Exact Solutions in Infinite Dimensions (Cambridge University Press, Cambridge, England).
- Parisi, G., and F. Zamponi, 2010, Rev. Mod. Phys. 82, 789.
- Pierangeli, D., A. Tavani, F. Di Mei, A. J. Agranat, C. Conti, and E. DelRe, 2017, Nat. Commun. 8, 1501.
- Pincheira, P. I. R., A. F. Silva, S. I. Fewo, S. J. M. Carreño, A. L. Moura, E. P. Raposo, A. S. L. Gomes, and C. B. de Araujo, 2016, Opt. Lett. 41, 3459.
- Regge, T., 1959, Nuovo Cimento 14, 951.
- Ruelle, D., 1987, Commun. Math. Phys. 108, 225.
- Sarkar, A., Shivakiran Bhaktha, and B. N. Andreasen, 2020, Sci. Rep. 10, 2628.
- Seguin, A., and Olivier Dauchot, 2016, Phys. Rev. Lett. 117, 228001.
- Shakhnovich, E., 2006, Chem. Rev. 106, 1559.
- Sherrington, D., and S. Kirkpatrick, 1975, Phys. Rev. Lett. 35, 1792.
- Symanzik, K., 1969, in Local Quantum Theory, edited by R. Jost (Academic Press, New York).
- Talagrand, M., 2003, C.R. Seances Acad. Sci. Ser. 1 337, 111, https://www.infona.pl/resource/bwmeta1.element.elsevier-53d9612e-ab91-36a7-a453-4b4eb4bdfda7.
- Talagrand, M., 2006, Ann. Math. 163, 221.
- Temesvári, T., I. Kondor, and C. De Dominicis, 2000, Eur. Phys. J. B 18, 493.
- Thouless, D. J., J. R. L. de Almeida, and J. M. Kosterlitz, 1980, J. Phys. C 13, 3271.
- Thouless, J., P. W. Anderson, and R. G. Palmer, 1977, Philos. Mag. 35, 137.
- Toulouse, G., 1977, Commun. Phys. 2, 115.
- Wang, Y., J. Shang, Y. Jin, and J. Zhang, 2022, Proc. Natl. Acad. Sci. U.S.A. 119, e2204879119.
- Wilson, K. G., and M. E. Fisher, 1972, Phys. Rev. Lett. 28, 240.
- Wyart, M., 2012, Phys. Rev. Lett. 109, 125502.
- Wyart, M., L. E. Silbert, S. R. Nagel, and T. A. Witten, 2005, Phys. Rev. E 72, 051306.
- Xiao, H., A. J. Liu, and D. J. Durian, 2022, Phys. Rev. Lett. 128, 248001.