WIAS Preprint No. 416, (1998)

Stochastic symmetry-breaking in a Gaussian Hopfield model



Authors

  • Bovier, Anton
  • van Enter, Aernout C. D.
  • Niederhauser, Beat

2010 Mathematics Subject Classification

  • 82B44 82C32

Keywords

  • Hopfield model, Gaussian disorder, metastates, chaotic size-dependence, extrema of gaussian processes

Abstract

We study a "two-pattern" Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomen is the random breaking of a rotation symmetry of the distribution of the disorder variables.

Appeared in

  • J. Stat. Phys. 95 (1999), pp. 181-213

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