We study the finite dimensional marginals of the Gibbs measure in the
Hopfield model at low temperature when the number of patterns, M, is
proportional to the volume with a sufficiently small proportionality constant
\a>0. It is shown that even when a single pattern is selected (by a magnetic
field or by conditioning), the marginals do not converge almost surely, but
only in law. The corresponding limiting law is constructed explicitly. We fit
our result in the recently proposed language of ``metastates'' which we discuss
in some length. As a byproduct, in a certain regime of the parameters \a and
\b (the inverse temperature), we also give a simple proof of Talagrand's [T1]
recent result that the replica symmetric solution found by Amit, Gutfreund, and
Sompolinsky [AGS] can be rigorously justified.Comment: 41pp, plain TE
