Spin Susceptibility Representation of the Pairing Interaction for the two-dimensional Hubbard Model

Using numerical dynamic cluster quantum Monte Carlo results, we study a simple approximation for the pairing interaction of a two-dimensional Hubbard model with an on-site Coulomb interaction $U$ equal to the bandwidth. We find that with an effective temperature dependent coupling $\Ub(T)$ and the numerically calculated spin susceptibility $\chi(K-K')$, the d-wave pairing interaction is well approximated by $\frac{3}{2} \Ub^2\chi(K-K')$.