We consider a gas of two species of fermions with population imbalance. Using the renormalization group in \(d=1+\epsilon\) spatial dimensions, we show that for spinless fermions and \(2>\epsilon>0\) 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.