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Glauber dynamics of the Little-Hopfield model

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Zeitschrift für Physik B Condensed Matter

Abstract

The Glauber dynamics of the Little-Hopfield model is studied analytically with the help of path-integrals recently introduced by Sommers. The results of Amit, Gutfreund and Sompolinsky concerning the statics of the Little-Hopfield model near saturation are dynamically verified. Their replica-symmetric solution corresponds exactly to the self-consistency equations of the long-time limits of some time-dependent functions emerging in our dynamical treatment. We also found their generalized Almeida-Thouless line where the solution becomes unstable. The time-dependent evolution of the macroscopic overlaps for a finite number of stored patterns is investigated and the problems arising for an infinite number of them are indicated.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-5000, Köln 41, Federal Republic of Germany

    H. Rieger, M. Schreckenberg & J. Zittartz

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  1. H. Rieger
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  2. M. Schreckenberg
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  3. J. Zittartz
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Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln

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Rieger, H., Schreckenberg, M. & Zittartz, J. Glauber dynamics of the Little-Hopfield model. Z. Physik B - Condensed Matter 72, 523–533 (1988). https://doi.org/10.1007/BF01314534

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  • DOI: https://doi.org/10.1007/BF01314534

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