The Ghirlanda–Guerra identities for mixed p-spin model

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...

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Bibliographic Details
Published inComptes rendus. Mathématique Vol. 348; no. 3; pp. 189 - 192
Main Author Panchenko, Dmitry
Format Journal Article
LanguageEnglish
Published Paris Elsevier SAS 01.02.2010
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
General mathematics
General, history and biography
Mathematics
Sciences and techniques of general use
Spin
Spin Hamiltonian
Mixed model
Average
Mathematics
Overlay
Power
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Summary: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 . 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).
ISSN:1631-073X
1778-3569
DOI:10.1016/j.crma.2010.02.004