A Spin Fluctuation Model for D-wave Superconductivity
  In this review we demonstrate that superconducting pairing, mediated by the exchange of spin fluctuations, is a viable alternative to conventional phonon-mediated pairing. We discuss in detail the normal state properties, the spin fluctuation induced d-wave pairing and the superconducting behavior of a material near an antiferromagnetic instability, when the dominant interaction between quasiparticles is of electronic origin, and at energies much smaller than the fermionic bandwidth, can be viewed as being due to the emission and absorption of a collective, soft spin degree of freedom. We show that in the vicinity of an antiferromagnetic quantum critical point the system behavior is universal, at least when the effective spin fermion interaction is smaller than the fermionic bandwidth. We further argue that spin-fluctuation exchange yields an attraction and pairing in the $d_{x^{2}-y^{2}}$ channel in agreement with what nearly all researchers now believe is the pairing symmetry in the cuprates. We discuss "fingerprints" of a spin mediated pairing state, chiefly associated with the emergence of the resonance peak in the spin response in a d-wave superconductor and identify these fingerprints in spectroscopic experiments on optimally doped cuprate superconconductors. 
Andrey V. Chubukov, David Pines, and Joerg Schmalian