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An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model


Bolthausen, Erwin (2014). An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model. Communications in Mathematical Physics, 325(1):333-366.

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.

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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Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics
Uncontrolled Keywords:Mathematical Physics, Statistical and Nonlinear Physics
Language:English
Date:1 January 2014
Deposited On:23 Jul 2019 09:50
Last Modified:15 Apr 2021 15:07
Publisher:Springer
ISSN:0010-3616
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s00220-013-1862-3

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