An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
Erwin Bolthausen
TL;DR
This paper introduces an iterative method for constructing solutions to the TAP equations in the SK model, with proven convergence up to the de Almayda-Thouless-line, but without addressing the model's broader properties.
Contribution
It presents a new iterative scheme for solving the TAP equations and proves its convergence within a specific parameter range.
Findings
Convergence of the iterative scheme is established up to the de Almayda-Thouless-line.
No new results are provided for the SK model beyond the solution construction.
The method offers a potential tool for analyzing the TAP equations in spin glass theory.
Abstract
We propose an iterative construction of solutions of the Thouless-Anderson-Palmer-equations for the Sherrington-Kirpatrick model. The iterative scheme is proved to converge exactly up to the de Almayda-Thouless-line. No results on the SK-model itself are derived.
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