CriticalbehavioroftheT=0 2kFdensity-wave phase transition in a two-dimensional Fermi liquid

We study T=0 spin-density-wave transitions in two-dimensional Fermi liquids in which the ordering wave vector Q is such that the tangents to the Fermi line at the points connected by Q are parallel (e.g., Q=2${\mathit{p}}_{\mathit{F}}$ in a system with a circular Fermi line) and the Fermi line is not flat. We show that the transition is first order if the ordering wave vector Q is not commensurate with a reciprocal lattice vector G, i.e., Q≠G/2. If Q is close to G/2 the transition is weakly first order and an intermediate scaling regime exists; in this regime the 2${\mathit{p}}_{\mathit{F}}$ susceptibility and observables such as the NMR rates ${\mathit{T}}_1$ and ${\mathit{T}}_2$ have scaling forms which we determine.