  We characterize the two-site marginals of exchangeable states of a system of
quantum spins in terms of a simple positivity condition. This result is used in
two applications. We first show that the distance between two-site marginals of
permutation invariant states on N spins and exchangeable states is of order
1/N. The second application relates the mean ground state energy of a
mean-field model of composite spins interacting through a product pair
interaction with the mean ground state energies of the components.
