  We consider a gas of two species of fermions with population imbalance. Using
the renormalization group in $d=1+\epsilon$ dimensions, we show that for
spinless fermions and $\epsilon > 0$ a fixed point appears at finite attractive
coupling where the quasiparticle residue vanishes, and identify this with the
transition to Larkin--Ovchinnikov--Fulde--Ferrell order (inhomogeneous
superconductivity). When the two species of fermions also carry spin degrees of
freedom we find a fixed point indicating a transition to spin density wave
order.
