Work

Quenched complexity of marginal states in the Sherrington--Kirkpatrick spin glass

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.04006

Authors: De Chirico, Tiziana, Leuzzi, Luca

Institutions: Istituto di Nanotecnologia, Sapienza University of Rome, National Research Council

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, HORIZON EUROPE European Innovation Council

OpenAlex ID: W7208838836

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