A dynamic cluster quantum Monte Carlo algorithm is used to study a spin-susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by $\frac{3}{2}\overline{U}{(T)}^{2}\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$, with an effective temperature and doping dependent coupling
U(T) and the numerically calculated spin susceptibility $\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$. We show that at low temperatures,
U may be accurately determined from a corresponding spin-susceptibility based calculation of the single-particle self-energy. We conclude that the strength of the
d-wave pairing interaction, characterized by the mean-field transition temperature, can be determined from a knowledge of the dressed spin susceptibility and the nodal quasiparticle spectral weight. This has important implications with respect to the questions of whether spin fluctuations are responsible for pairing in the high-
Tc cuprates.
Using Monte Carlo simulations, we have studied the question of phase separation and pairing in the doped two-dimensional Hubbard model. For a range of U/t values greater than as well as less than the bandwidth, we find no evidence for phase separation when the system is doped away from half filling. In agreement with previous work, we find that the d-wave and extended s-wave pairing correlations are enhanced by the interaction vertex but that none of the eight different pairing correlations that we studied increases as a function of lattice size. We have also examined the dependence of the kinetic energy, which determines the total optical spectral weight, on U/t and filling 〈n〉.