PreprintarXiv licencearXiv
Free energy and spectral edge of the SYK model
Abstract
Consider the Sachdev-Ye-Kitaev model with N Majorana fermions and interaction order q. For even 4≤ q≪ √N, we present a microscopic framework that determines the free energy limit at every fixed inverse temperature β>0. In particular, this gives the first rigorous derivation of the Schwinger-Dyson thermodynamics of the model. For all even q∈ {4,6,...,N−4}, we further determine the asymptotic location of the largest eigenvalue, which answers a question posed by Feng-Tian-Wei \cite{FengTianWei1}. Consequently, we obtained the free energy limit along every sequence β≡ βN→∞.
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BibTeX
@misc{he2026free,
title = {{Free energy and spectral edge of the SYK model}},
author = {Yukun He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.18998},
eprint = {2607.18998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18998},
}
RIS
TY - UNPB
TI - Free energy and spectral edge of the SYK model
AU - Yukun He
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2607.18998
UR - https://arxiv.org/abs/2607.18998
AB - Consider the Sachdev-Ye-Kitaev model with N Majorana fermions and interaction order q. For even 4≤ q≪ √N, we present a microscopic framework that determines the free energy limit at every fixed inverse temperature β>0. In particular, this gives the first rigorous derivation of the Schwinger-Dyson thermodynamics of the model. For all even q∈ {4,6,...,N−4}, we further determine the asymptotic location of the largest eigenvalue, which answers a question posed by Feng-Tian-Wei \cite{FengTianWei1}. Consequently, we obtained the free energy limit along every sequence β≡ β_N→∞.
ER -