PreprintCC BY 4.0arXiv
Free energy fluctuation of soft spherical Sherrington-Kirkpatrick model
Abstract
We consider a soft version of the spherical Sherrington-Kirkpatrick model, where the spherical constraint is replaced by a radial confinement term. We prove that, for a real symmetric disorder matrix under suitable spectral assumptions, the free energy exhibits two distinct fluctuation regimes. In the high-temperature regime, the fluctuations are asymptotically Gaussian. In the low-temperature regime, the fluctuations are governed by the largest eigenvalue and converge to the GOE Tracy-Widom distribution. These results show that the soft radial constraint preserves the fluctuation transition of the classical spherical Sherrington-Kirkpatrick model.
Related
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BibTeX
@misc{lee2026free,
title = {{Free energy fluctuation of soft spherical Sherrington-Kirkpatrick model}},
author = {Ji Oon Lee and Seongcheol Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17971},
eprint = {2609.17971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17971},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Free energy fluctuation of soft spherical Sherrington-Kirkpatrick model
AU - Ji Oon Lee
AU - Seongcheol Lee
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.17971
UR - https://arxiv.org/abs/2609.17971
AB - We consider a soft version of the spherical Sherrington-Kirkpatrick model, where the spherical constraint is replaced by a radial confinement term. We prove that, for a real symmetric disorder matrix under suitable spectral assumptions, the free energy exhibits two distinct fluctuation regimes. In the high-temperature regime, the fluctuations are asymptotically Gaussian. In the low-temperature regime, the fluctuations are governed by the largest eigenvalue and converge to the GOE Tracy-Widom distribution. These results show that the soft radial constraint preserves the fluctuation transition of the classical spherical Sherrington-Kirkpatrick model.
ER -