A highly accurate theoretical approach, based on exact and quasiexact sum rules, is presented for the averaged two-body correlation function of the hard-disk solid. Excellent results are obtained as compared to computer simulations for this function. However, when these results are used as the basis for a first-order perturbation theory, the phase diagram of the two-dimensional square-well model potential is only reproduced qualitatively, showing that higher-order correlation terms play a non-negligible role in two dimensions.