Gap anisotropy and universal pairing scale in a spin-fluctuation model of cuprate superconductors

We consider the evolution of dₗ^{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 couplings passing through a broad maximum at intermediate coupling. At strong coupling, T^ is of order of 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.