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 and .
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).
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Dmitry Panchenko 1
@article{CRMATH_2010__348_3-4_189_0, 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}, }
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/
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