The TAP approach to intensive and extensive connectivity systems


The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.

Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: Copyright of the Massachusetts Institute of Technology Press (MIT Press) Partially available on Google Books
Uncontrolled Keywords: Thouless-Anderson-Palmer,Sherrington-Kirkpatrick,general intensively connected systems,Hopfield associative memory model
ISBN: 0262150549
Last Modified: 13 Jun 2024 07:43
Date Deposited: 05 Aug 2009 12:02
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Related URLs: http://mitpress ... type=2&tid=3847 (Publisher URL)
PURE Output Type: Chapter
Published Date: 2001-02
Authors: Kabashima, Yoshiyuki
Saad, David (ORCID Profile 0000-0001-9821-2623)



Version: Accepted Version

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