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The Mézard-Parisi formula
Abstract
This paper proves the Mézard-Parisi formula for the free energy of random K-sat and diluted p-spin models with even p, completing an approach developed in earlier work of the author and collaborators. The upper bound was established by Franz and Leone. Here the matching lower bound is proved for a general class of diluted models under symmetry and integrability assumptions. The main new contribution is a proof of an approximate form of the Mézard-Parisi reproducibility hypothesis without assuming that the overlap distribution has finite support.
Related
- Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians
- Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model
- Parisi measure of the Sherrington-Kirkpatrick model with external field
- Rigorous frozen-scale estimates for the Parisi–Zamponi matching front: the confined-spine adaptation of Schertzer–Tourniaire
- Upper deviations of the Sherrington-Kirkpatrick free energy: the fifth-order law and the onset of constrained Parisi measures
BibTeX
@misc{panchenko2026mézardparisi,
title = {{The Mézard-Parisi formula}},
author = {Dmitry Panchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39545},
eprint = {2610.39545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39545},
}
RIS
TY - UNPB
TI - The Mézard-Parisi formula
AU - Dmitry Panchenko
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39545
UR - https://arxiv.org/abs/2610.39545
AB - This paper proves the Mézard-Parisi formula for the free energy of random K-sat and diluted p-spin models with even p, completing an approach developed in earlier work of the author and collaborators. The upper bound was established by Franz and Leone. Here the matching lower bound is proved for a general class of diluted models under symmetry and integrability assumptions. The main new contribution is a proof of an approximate form of the Mézard-Parisi reproducibility hypothesis without assuming that the overlap distribution has finite support.
ER -