Spin-fermion model near the quantum critical point: one-loop renormalization group results

The properties of the antiferromagnetic quantum critical point for itinerant electrons were explored by expanding in the inverse number of hot spots in the Brillouin zone N = 8. By going beyond a self-consistent N = ∞ theory, it was found that the Fermi surface becomes nested at hot spots which is a weak spin-density wave (SDW) precursor effect, and vertex corrections account for anomalous spin dynamics and change the dynamical critical exponent from z = 2 to z > 2. To first order in 1/N, z = 2N/(N - 2) ≈ 2.67 was found.