IDEAS home Printed from
   My bibliography  Save this article

The Hopfield model with superlinearly many patterns


  • Zhao, James Y.


We study the Hopfield model where the ratio α of patterns to sites grows large. We prove that the free energy with inverse temperature β and external field B behaves like βα+γ, where γ=P(2β,B) is the limiting free energy of the Sherrington–Kirkpatrick model with inverse temperature 2β and external field B.

Suggested Citation

  • Zhao, James Y., 2013. "The Hopfield model with superlinearly many patterns," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 350-356.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:350-356
    DOI: 10.1016/j.spl.2012.09.026

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Gentz, Barbara, 1996. "An almost sure central limit theorem for the overlap parameters in the Hopfield model," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 243-262, July.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Hopfield model; Free energy; Mean field models;


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:350-356. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.