Zeitschrift für Physik B Condensed Matter

, Volume 72, Issue 4, pp 523–533 | Cite as

Glauber dynamics of the Little-Hopfield model

  • H. Rieger
  • M. Schreckenberg
  • J. Zittartz


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.


Spectroscopy Neural Network State Physics Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • H. Rieger
    • 1
  • M. Schreckenberg
    • 1
  • J. Zittartz
    • 1
  1. 1.Institut für Theoretische PhysikUniversität zu KölnKöln 41Federal Republic of Germany

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