The Ghirlanda-Guerra identities for mixed p-spin model

Details The Ghirlanda-Guerra identities for mixed p-spin model The Ghirlanda-Guerra identities for mixed p-spin model

2010-02-10

arxiv.org/abs/1002.2190v1

C.R.Acad.Sci.Paris, Ser. I 348 (2010) 189-192.

Mathematics

Probability

Scientific paper

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 $p$th 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 $p\geq 2$ and $p=1.$

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