Comptes Rendus
Probability Theory/Mathematical Physics
The Ghirlanda–Guerra identities for mixed p-spin model
Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 189-192.

We show that, under the conditions known to imply the validity of the Parisi formula, if the generic Sherrington–Kirkpatrick Hamiltonian contains a p-spin term then the Ghirlanda–Guerra identities for the pth power of the overlap hold in a strong sense without averaging. This implies strong version of the extended Ghirlanda–Guerra identities for mixed p-spin models than contain terms for all even p2 and p=1.

Nous montrons que sous les conditions connues pour impliquer la validité de la formule de Parisi, si l'Hamiltonien du modè le générique de Sherrington–Kirkpatrick Hamiltonien contient un « Hamiltonien de p-spin » alors les identités de Ghirlanda–Guerra pour la puissance p des recouvrements sont valides dans un sens fort (et pas seulement en moyenne sur les parametres).

Published online:
DOI: 10.1016/j.crma.2010.02.004

Dmitry Panchenko 1

1 Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA
     author = {Dmitry Panchenko},
     title = {The {Ghirlanda{\textendash}Guerra} identities for mixed \protect\emph{p}-spin model},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {189--192},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2010.02.004},
     language = {en},
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PB  - Elsevier
DO  - 10.1016/j.crma.2010.02.004
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Dmitry Panchenko. The Ghirlanda–Guerra identities for mixed p-spin model. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 189-192. doi : 10.1016/j.crma.2010.02.004.

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