The Ghirlanda-Guerra identities for mixed p-spin model

TL;DR

This paper proves that the Ghirlanda-Guerra identities hold strongly for mixed p-spin models under conditions ensuring the Parisi formula, extending the identities to all even p and p=1 without averaging.

Contribution

It establishes strong Ghirlanda-Guerra identities for mixed p-spin models, including all even p and p=1, under conditions related to the Parisi formula validity.

Findings

Ghirlanda-Guerra identities hold strongly without averaging

Identifies conditions under which identities are valid for mixed p-spin models

Extends identities to all even p and p=1 in the models

Abstract

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 $p=1.$