Spin-Fermion Model near the Quantum Critical Point: One-Loop Renormalization Group Results

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, $N$, and present the results beyond the previously studied $N=\infty$ limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from $z=2\mathrm{}$ to $z>\mathrm{}2\mathrm{}$. To first order in $1/N$ we found $z=2N/(N-2\mathrm{})$ which for a physical $N=8\mathrm{}$ yields $z\approx 2.67$.