Comptes Rendus
Probability Theory/Mathematical Physics
The generalized Parisi formula
Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 111-114.

For a large class of Gaussian Hamiltonians, we use Guerra's interpolation scheme to show that at any temperature the free energy of the corresponding spin-glass system is asymptotically given by Parisi's formula. This class includes the Sherrington–Kirkpatrick model, the p-spin interaction model for even p, and many others.

Pour une large classe d'Hamiltoniens Gaussiens, nous utilisons la méthode d'interpolation de Guerra pour montrer qu'à toute température l'énergie libre du verre spin correspondant est donnée par la formule de Parisi. Cette classe comprend le modèle de Sherrington–Kirkpatrick, le modèle à p-spin pour p pair, et bien d'autres.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00268-1
Michel Talagrand 1

1 Équipe d'analyse de l'institut mathématique, 4, place Jussieu, 75230 Paris cedex 05, France
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Michel Talagrand. The generalized Parisi formula. Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 111-114. doi : 10.1016/S1631-073X(03)00268-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00268-1/

[1] F. Guerra Replica broken bounds in the mean field spin glass model, Comm. Math. Phys., Volume 233 (2003), pp. 1-12

[2] M. Talagrand Multiple levels of symmetry breaking, Probab. Theory Related Fields, Volume 117 (2000), pp. 449-466

[3] M. Talagrand Spin Glasses: A Challenge to Mathematicians, Springer-Verlag, 2003

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