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.
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