J. Phys. I France
Volume 2, Numéro 3, March 1992
Page(s) 247 - 250
DOI: 10.1051/jp1:1992140
J. Phys. I France 2 (1992) 247-250

Reetrant spin glass behaviour in the replica symmetric solution of the Hopfield neural network model

Jean-Pierre Naef and Andrew Canning

Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland

(Received 18 November 1991, accepted 6 December 1991)

Numerical and analytical solutions at low temperature are presented for the replica symmetric order parameter equations of the Hopfield neural model with interactions between all the spins. We find that these equations give weak reentrant spin glass behaviour at T<0.023. This is similar behaviour to that found for the replica symmetric solution of the SK spin glass [4] although in that case the reentrant phase is much larger. It is also known from what is believed to be the true solution for the SK spin glass that this reentrant behaviour is unphysical so, by analogy, we believe it is unphysical for neural network models. Even so, the maximum value in replica theory of $\alpha_{\rm c}$, which measures the storage capacity of the Hopfield model, is to be found at $\alpha_{\rm c}(T=0.023)=0.1382$. This is slightly higher than the zero temperature value of $\alpha_{\rm c}(T=0)=0.1379$

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