Capacity of the Hopfield model

For a given 0 < δ < 2 if [Nδ] neurons deviating from the memorized patterns are allowed, we constructively show that if and only if α(δ) := p(N)/N = (1 − 2δ)2/(1 − δ)2 all stored patterns are fixed points of the Hopfield model. If [NδN ] neurons are allowed with δN → 0 then αN = (1−2δN )2/(8−1(1−δN ))2 → 0 where 8 is the distribution function of the normal distribution. The result obtained by Amit and co-workers only formally coincides with the latter case which indicates that the replica trick approach to the capacity of the Hopfield model is only valid in the case αN → 0(N →∞).