  We estimate the critical capacity of the zero-temperature Hopfield model by
using a novel and rigorous method. The probability of having a stable fixed
point is one when $\alpha\le 0.113$ for a large number of neurons. This result
is an advance on all rigorous results in the literature and the relationship
between the capacity $\alpha$ and retrieval errors obtained here for small
$\alpha$ coincides with replica calculation results.
