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2022 TAP equations are repulsive
Stephan Gufler, Jan Lukas Igelbrink, Nicola Kistler
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Electron. Commun. Probab. 27: 1-7 (2022). DOI: 10.1214/22-ECP505

Abstract

We show that for low enough temperatures, but still above the AT line, the Jacobian of the TAP equations for the SK model has a macroscopic fraction of eigenvalues outside the unit interval. This provides a simple explanation for the numerical instability of the fixed points, which thus occurs already in high temperature. The insight leads to some algorithmic considerations on the low temperature regime.

Funding Statement

This work has been supported by Deutsche Forschungsgemeinschaft (DFG) - project number 432176920.

Acknowledgments

We acknowledge the Allianz für Hochleistungsrechnen Rheinland-Pfalz for granting us access to the High Performance Computing Elwetritsch, on which our numerical simulations have been performed. It is furthermore a pleasure to thank Yan V. Fyodorov, Giorgio Parisi, Timm Plefka, Federico Ricci-Tersenghi and Marius A. Schmidt for enlightening conversations.

Citation

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Stephan Gufler. Jan Lukas Igelbrink. Nicola Kistler. "TAP equations are repulsive." Electron. Commun. Probab. 27 1 - 7, 2022. https://doi.org/10.1214/22-ECP505

Information

Received: 23 August 2022; Accepted: 11 December 2022; Published: 2022
First available in Project Euclid: 19 December 2022

Digital Object Identifier: 10.1214/22-ECP505

Subjects:
Primary: 82B44
Secondary: 60B20

Keywords: Spin glasses , TAP equations

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