The $\mathbf{T}=0$ $2{\mathbf{k}}_{\mathbf{F}}$ density wave phase transition in a two dimensional Fermi liquid is first order

Abstract

We study $T=0$ spin density wave transitions in two dimensional Fermi liquids in which the ordering wavevector $\mathbf{Q}$ is such that the tangents to the Fermi line at the points connected by $\mathbf{Q}$ are parallel (e.g. $Q=2p_F$ 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 $\mathbf{Q}$ is not commensurate with a reciprocal lattice vector, $\mathbf{G}$, i.e. $\mathbf{Q}\ne \mathbf{G}/2$. If $\mathbf{Q}$ is close to $\mathbf{G}/2$ the transition is weakly first order and an intermediate scaling regime exists; in this regime the $2p_F$ susceptibility and observables such as the NMR rates $T_1$ and $T_2$ have scaling forms which we determine.

11 pages, 8 Postscript figures in a separate file