Reetrant spin glass behaviour in the replica symmetric solution of the Hopfield neural network model
Jean-Pierre Naef, Andrew Canning · Journal de Physique I · 1992
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 αc, which measures the storage capacity of the Hopfield model, is to be found at αc(T=0.023)=0.1382. This is slightly higher than the zero temperature value of αc(T=0)=0.1379