The Ghirlanda–Guerra identities for mixed <i>p</i>-spin model

Dmitry Panchenko

doi:10.1016/j.crma.2010.02.004

Probability Theory/Mathematical Physics

The Ghirlanda–Guerra identities for mixed p-spin model
[Les identités de Ghirlanda–Guerra pour les mélanges de modèles à p-spin]

Présenté par : Michel Talagrand

Dmitry Panchenko ¹

¹ Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA

Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 189-192.

Résumé
Abstract

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).

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 $p ⩾ 2$ and $p = 1$ .

Reçu le : 2010-01-31
Accepté le : 2010-02-03
Publié le : 2010-02-01

DOI : 10.1016/j.crma.2010.02.004

Affiliations des auteurs :

Dmitry Panchenko ¹

¹ Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA

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     title = {The {Ghirlanda{\textendash}Guerra} identities for mixed \protect\emph{p}-spin model},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {189--192},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.02.004/

Bibliographie
Cité par

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[3] D. Panchenko On differentiability of the Parisi formula, Electron. Comm. Probab., Volume 13 (2008), pp. 241-247

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[7] M. Talagrand, Construction of pure states in mean-field models for spin glasses, preprint (2008), Probab. Theory Related Fields, in press, http://www.springerlink.com/content/y507332m08275t67/?p=d35ca639b02943ecae07559b26ef2abf&pi=10

[8] M. Talagrand, Mean field models for spin glasses, manuscript

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