Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates

We consider the evolution of $d_{x^2-y^2}$ pairing, mediated by nearly critical spin fluctuations, with the coupling strength. We show that the onset temperature for pairing, $T^*$, smoothly evolves between weak and strong coupling, passing through a broad maximum at intermediate coupling. At strong coupling, $T^*$ is of order the magnetic exchange energy $J$. We argue that for all couplings, pairing is confined to the vicinity of the Fermi surface. We also find that thermal spin fluctuations only modestly reduce $T^*$, even at criticality, but they substantially smooth the gap anisotropy. The latter evolves with coupling, being the largest at weak coupling.