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Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model
Abstract
We establish quantitative Parisi formulas and fluctuation bounds for the Sherrington-Kirkpatrick model at zero external field. In particular, using that the Parisi measure is supported on an interval, we show that for every fixed inverse temperature greater than one, the variance of the logarithmic partition function lies between orders N4/15 and N7/15. The same exponents hold for the ground-state variance. We also obtain upper and lower bounds on the finite-size bias of the mean free energy and ground-state energy, together with two-sided upper-tail estimates with exponent 6/5 at both positive and zero temperature.
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BibTeX
@misc{aronow2026quantitative,
title = {{Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model}},
author = {P. M. Aronow and Patrick Lopatto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09103},
eprint = {2609.09103},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09103},
}
RIS
TY - UNPB
TI - Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model
AU - P. M. Aronow
AU - Patrick Lopatto
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09103
UR - https://arxiv.org/abs/2609.09103
AB - We establish quantitative Parisi formulas and fluctuation bounds for the Sherrington-Kirkpatrick model at zero external field. In particular, using that the Parisi measure is supported on an interval, we show that for every fixed inverse temperature greater than one, the variance of the logarithmic partition function lies between orders N^4/15 and N^7/15. The same exponents hold for the ground-state variance. We also obtain upper and lower bounds on the finite-size bias of the mean free energy and ground-state energy, together with two-sided upper-tail estimates with exponent 6/5 at both positive and zero temperature.
ER -