The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model
Abstract
We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington\--Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quantum SK (QSK) model. In particular, we determine the phase boundary separating the glassy and paramagnetic phases explicitly. Such an analytic characterization of the glass transition is not expected for the true QSK and even unknown for most vector glass models. Despite being of independent interest, the analysis of the self-overlap corrected QSK model serves as important ingredient in the characterization of paramagnetic behavior in the real QSK. The proof is based on a simplified Parisi variational principle for the quantum pressure, which only involves classical Parisi order parameters. As part of the proof, we also analyze the pressure of the self-overlap-constrained quantum SK model and its Parisi description, as well as the pressure of generalized quantum Hopfield models.
Related
- A quantitative replica-symmetric bound for Sherrington--Kirkpatrick model in the entire de Almeida--Thouless region
- Sampling from the Sherrington-Kirkpatrick Model up to Criticality
- Free energy and fluctuations of generalized bipartite Sherrington-Kirkpatrick models and generalized Hopfield models
- Free energy fluctuation of soft spherical Sherrington-Kirkpatrick model
- Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model
BibTeX
@misc{manai2026quantum,
title = {{The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model}},
author = {Chokri Manai and Simone Warzel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.19800},
eprint = {2605.19800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19800},
}
RIS
TY - UNPB
TI - The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model
AU - Chokri Manai
AU - Simone Warzel
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2605.19800
UR - https://arxiv.org/abs/2605.19800
AB - We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington\--Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quantum SK (QSK) model. In particular, we determine the phase boundary separating the glassy and paramagnetic phases explicitly. Such an analytic characterization of the glass transition is not expected for the true QSK and even unknown for most vector glass models. Despite being of independent interest, the analysis of the self-overlap corrected QSK model serves as important ingredient in the characterization of paramagnetic behavior in the real QSK. The proof is based on a simplified Parisi variational principle for the quantum pressure, which only involves classical Parisi order parameters. As part of the proof, we also analyze the pressure of the self-overlap-constrained quantum SK model and its Parisi description, as well as the pressure of generalized quantum Hopfield models.
ER -