The $\bf T=0$ $\bf 2k_F$ density wave phase transition in a two dimensional Fermi liquid is first order

TL;DR

This paper investigates the nature of zero-temperature spin density wave transitions in two-dimensional Fermi liquids, revealing that such transitions are generally first order unless the wavevector is commensurate with the lattice, with a weakly first order regime near commensurability.

Contribution

The study demonstrates that $T=0$ spin density wave transitions in 2D Fermi liquids are predominantly first order, providing detailed analysis of the scaling behavior near commensurate wavevectors.

Findings

Transition is first order if Q is not commensurate with G.

Near commensurability, the transition is weakly first order with a scaling regime.

Scaling forms for susceptibility and NMR observables are derived.

Abstract

We study $T=0$ spin density wave transitions in two dimensional Fermi liquids in which the ordering wavevector $\bf Q$ is such that the tangents to the Fermi line at the points connected by $\bf Q$ 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 $\bf Q$ is not commensurate with a reciprocal lattice vector, $\bf G$, i.e. ${\bf Q} \neq {\bf G}/2$. If $\bf Q$ is close to ${\bf G}/2$ 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.