FIG. 4: Dep endence of T$_{c}$/T$_{c}$$_{0}$ and Δ / Δ$_{0}$ on inelastic scattering for the case of d-wave pairing. An Einstein sp ectrum of spin-fluctutations at ω$_{E}$ is used for simplicity with frequencies 1 and additional Einstein modes are introduced with frequencies (in units of ω$_{E}$ ) as marked for cu rves a, b and c. T$_{c}$$_{0}$ , and Δ$_{0}$ are the values without inelastic scattering and so is the unmarked curv e. Dashed and full lines represent approximate and exact solutions of the Eliashberg equations. For details, see (23) C. Quantum-Criticality in Relation to T$_{c}$ in e-e Induced Pairing The highest T$_{c}$ ’s in the Cuprates are undoubtedly through electronic fluctuations, and near a quantum-critical point (qcp), as are those in the heavy-fermions. This as we will see is likely be true for the pncitides as well. As discussed below for each of these cases, we know this because the observed transport and thermodynamic properties for T ⩾ T$_{c}$ in these compounds can only be understood as due to scattering of fermions from fluctuations which have a singularity in the limit ω → 0 , T → 0. It is therefore important to ask about the role of spectral distribution of fluctuations near qcp’s in determining T$_{c}$ in light of what we have learnt in the previous section. Much less is understood about the universality classes of quantum critical points (qcp) than classical critical points where the scale-invariant frequency and momentum dependence of critical fluctuations for the classical critical points has been catalogued into different Uni- versality classes [27]. A qcp is the point p = p$_{c}$ , where by varying a parameter p , for example pressure or electron density, the transition temperature to some broken symmetry → 0. A 22