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The anomalous transport and thermodynamic properties in the quantum-criticalregion, in the cuprates, and in the quasi-two dimensional Fe-basedsuperconductors and heavy-fermion compounds, have the same temperaturedependences. This can occur only if, despite their vast microscopicdifferences, a common statistical mechanical model describes their phasetransitions. The antiferromagnetic (AFM)-ic models for the latter two, just asthe loop-current model for the cuprates, map to the dissipative XY model. Thesolution of this model in 2+1 D reveals that the critical fluctuations aredetermined by topological excitations, vortices and a variety of instantons,and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type,adapted by Moriya, Hertz and others for quantum-criticality. The absorptivepart of the fluctuations is a separable function of momentum ${\bf q}$,measured from the ordering vector, and of the frequency $\omega$ and thetemperature $T$ which scale as $\tanh(\omega/2T)$ at criticality. Directmeasurements of the fluctuations by neutron scattering in thequasi-two-dimensional heavy fermion and Fe-based compounds, near theirantiferromagnetic quantum critical point, are consistent with this form. Suchfluctuations, together with the vertex coupling them to fermions, lead to amarginal fermi-liquid, with the imaginary part of the self-energy $\proptomax(\omega, T)$ for all momenta, a resistivity $\propto T$, a $T \ln T$contribution to the specific heat, and other singular fermi-liquid propertiescommon to these diverse compounds, as well as to d-wave superconductivity. Thisis explicitly verified, in the cuprates, by analysis of the pairing and thenormal self-energy directly extracted from the recent high resolution angleresolved photoemission measurements.

Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates