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Ghirlanda-Guerra identities and cavity equations for diluted spin glass models

  • Dmitry Panchenko
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Abstract

This note supplies the details of the cavity lower bound used in "The Mézard-Parisi formula" [8]. Specifically, we show that small perturbations that do not change the limiting free energy can be chosen so that the asymptotic Gibbs measures arising in the Aizenman-Sims-Starr lower bound satisfy both the Ghirlanda-Guerra identities and the cavity equations. These calculations are standard and require only minor modifications of arguments already available in the literature. We record them here for completeness, avoiding a lengthy repetition of these arguments in [8].

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Cite

BibTeXRIS
BibTeX
@misc{panchenko2026ghirlandaguerra,
  title = {{Ghirlanda-Guerra identities and cavity equations for diluted spin glass models}},
  author = {Dmitry Panchenko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39542},
  eprint = {2610.39542},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39542},
}
RIS
TY  - UNPB
TI  - Ghirlanda-Guerra identities and cavity equations for diluted spin glass models
AU  - Dmitry Panchenko
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39542
UR  - https://arxiv.org/abs/2610.39542
AB  - This note supplies the details of the cavity lower bound used in "The Mézard-Parisi formula" [8]. Specifically, we show that small perturbations that do not change the limiting free energy can be chosen so that the asymptotic Gibbs measures arising in the Aizenman-Sims-Starr lower bound satisfy both the Ghirlanda-Guerra identities and the cavity equations. These calculations are standard and require only minor modifications of arguments already available in the literature. We record them here for completeness, avoiding a lengthy repetition of these arguments in [8].
ER  -