PreprintCC BY 4.0arXiv
Quenched complexity of marginal states in the Sherrington--Kirkpatrick spin glass
Abstract
The number of metastable states of a random corrugated landscape controls what dynamics, inference and learning can reach. In the Sherrington-Kirkpatrick model these states are marginal, and counting them requires breaking the BRST symmetry. So far only the annealed complexity was known, predicting states below equilibrium. We compute the quenched complexity function with a two-group Ansatz and one-step replica symmetry breaking. It branches continuously off the annealed curve at its instability point and vanishes near the Parisi free energy, while the soft mode turns toward orthogonality to the magnetization.
Related
- Sampling from the Sherrington-Kirkpatrick Model up to Criticality
- Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature
- Glauber dynamics of the Sherrington--Kirkpatrick spin-glass model: a dynamical cavity method
- Critical Free-Energy Variance in the Sherrington-Kirkpatrick Model
- Parisi's solution of the Sherrington--Kirkpatrick model from synchronous Monte Carlo dynamics
BibTeX
@misc{chirico2026quenched,
title = {{Quenched complexity of marginal states in the Sherrington--Kirkpatrick spin glass}},
author = {Tiziana De Chirico and Luca Leuzzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.04006},
eprint = {2609.04006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04006},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quenched complexity of marginal states in the Sherrington--Kirkpatrick spin glass
AU - Tiziana De Chirico
AU - Luca Leuzzi
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.04006
UR - https://arxiv.org/abs/2609.04006
AB - The number of metastable states of a random corrugated landscape controls what dynamics, inference and learning can reach. In the Sherrington-Kirkpatrick model these states are marginal, and counting them requires breaking the BRST symmetry. So far only the annealed complexity was known, predicting states below equilibrium. We compute the quenched complexity function with a two-group Ansatz and one-step replica symmetry breaking. It branches continuously off the annealed curve at its instability point and vanishes near the Parisi free energy, while the soft mode turns toward orthogonality to the magnetization.
ER -