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The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann.
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Parisi, GiorgioG. (1980). A sequence of approximate solutions to the S-K model for spin glasses. J. Phys. A 13 L–115
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Mézard, M.M., Parisi, G.G., Sourlas, N.N., Toulouse, G.G. andVirasoro, M.M. (1984). Replica symmetry breaking and the nature of the spin glass phase. J. Physique 45 843–854
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Mézard, M.M., Parisi, G.G., Sourlas, N.N., Toulouse, G.G. andVirasoro, M. A.M. A. (1984). On the nature of the spin-glass phase. Phys. Rev. Lett. 52 1156
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Bolthausen, E.E. andSznitman, A. S.A. S. (1998). On Ruelle’s probability cascades and an abstract cavity method. Comm. Math. Phys. 197 247–276
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Ghirlanda, StefanoS. andGuerra, FrancescoF. (1998). General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity. J. Phys. A 31 9149–9155
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Baffioni, F.F. andRosati, F.F. (2000). Some exact results on the ultrametric overlap distribution in mean field spin glass models. Eur. Phys. J. B 17 439–447
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Aizenman, M.M., Sims, R.R. andStarr, S.S. (2003). An extended variational principle for the SK spin-glass model. Phys. Rev. B 68 214403
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Guerra, FrancescoF. (2003). Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys. 233 1–12
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Talagrand, MichelM. (2003). On Guerra’s broken replica-symmetry bound. C. R. Math. Acad. Sci. Paris 337 477–480
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Talagrand, MichelM. (2006). The Parisi formula. Ann. of Math. (2) 163 221–263
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Panchenko, DmitryD. (2010). The Ghirlanda–Guerra identities for mixed p p -spin model. C. R. Math. Acad. Sci. Paris 348 189–192
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Later among the works it cites.
Talagrand, MichelM. (2010). Construction of pure states in mean field models for spin glasses. Probab. Theory Related Fields 148 601–643
2010
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Panchenko, DmitryD. (2011). Ghirlanda–Guerra identities and ultrametricity: An elementary proof in the discrete case. C. R. Math. Acad. Sci. Paris 349 813–816
2011
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Talagrand, MichelM. (2011). Mean Field Models for Spin Glasses. Volume I. Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics] 54. Springer, Berlin
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Panchenko, D.D. (2013). The Sherrington–Kirkpatrick Model. Springer, New York
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Panchenko, DmitryD. (2007). A note on Talagrand’s positivity principle. Electron. Commun. Probab. 12 401–410 (electronic)
2007
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Arguin, Louis-PierreL.-P. andAizenman, MichaelM. (2009). On the structure of quasi-stationary competing particle systems. Ann. Probab. 37 1080–1113
2009
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Panchenko, DmitryD. (2010). A connection between the Ghirlanda–Guerra identities and ultrametricity. Ann. Probab. 38 327–347
2010
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Panchenko, DmitryD. (2010). On the Dovbysh–Sudakov representation result. Electron. Commun. Probab. 15 330–338
2010
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2013
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Panchenko, D.D. (2013). Spin glass models from the point of view of spin distributions. Ann. Probab. 41 1315–1361
2013
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Panchenko, DmitryD. (2013). The Parisi ultrametricity conjecture. Ann. of Math. (2) 177 383–393
2013
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Arguin, L. P.L. P. andChatterjee, S.S. (2014). Random overlap structures: Properties and applications to spin glasses. Probab. Theory Related Fields 156 375–413
2014
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