We study a Hopfield model whose number of patterns M grows to infinity with
the system size N, in such a way that M(N)(2) log M(N)IN tends to zero. In
this model the unbiased Gibbs state in volume N can essentially be decompo
sed into M(N) pairs of disjoint measures. We investigate the distributions
of the corresponding weights, and show, in particular, that these weights c
oncentrate for any given N very closely to one of the pairs, with probabili
ty tending to 1. Our analysis is based upon a new result on the asymptotic
distribution of order statistics of certain correlated exchangeable random
variables.