Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis

We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum critical point, in the marginal case of two dimensions (d=2,z=2). Up to next-to-leading order in the number of components (N) of the field, we find that logarithmic corrections do not lead to an enhancement of the Landau damping. This is in agreement with a renormalization-group analysis, for arbitrary N. Hence, the logarithmic effects are unable to account for the behavior reportedly observed in inelastic neutron scattering experiments on CeCu_{6-x}Au_x. We also examine the extended dynamical mean-field treatment (local approximation) of this theory, and find that only subdominant corrections to the Landau damping are obtained within this approximation, in contrast to recent claims.