Abstract
We propose an iterative scheme for the solutions of the TAP-equations in the Sherrington–Kirkpatrick model which is shown to converge up to and including the de Almeida–Thouless line. The main tool is a representation of the iterations which reveals an interesting structure of them. This representation does not depend on the temperature parameter, but for temperatures below the de Almeida–Thouless line, it contains a part which does not converge to zero in the limit.
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Communicated by F. Toninelli
Supported by an SNF grant No 200020-125247, and by the Humboldt Society.
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Bolthausen, E. An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model. Commun. Math. Phys. 325, 333–366 (2014). https://doi.org/10.1007/s00220-013-1862-3
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DOI: https://doi.org/10.1007/s00220-013-1862-3