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

Abstract

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 $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$ 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 $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ to $z>2$. To first order in $1/N$ we found $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2N/(N\ensuremath{-}2)$ which for a physical $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8$ yields $z\ensuremath{\approx}2.67$.