Abstract
For a given ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img5.gif
if ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img6.gif
neurons deviating from the memorized patterns are
allowed, we constructively show that if and only if
##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img7.gif
all stored patterns are fixed points of the Hopfield
model. If ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img8.gif
neurons are allowed with ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img9.gif
then ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img10.gif
where ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img11.gif
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 ##IMG##
http://ej.iop.org/images/0305-4470/30/10/016/img12.gif
.
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