Ferromagnetic Luttinger Liquids

We study weak itinerant ferromagnetism in one-dimensional Fermi systems using perturbation theory and bosonization. We find that longitudinal spin fluctuations propagate ballistically with velocity v_m << v_F, where v_F is the Fermi velocity. This leads to a large anomalous dimension in the spin-channel and strong algebraic singularities in the single-particle spectral function and in the transverse structure factor for momentum transfers q ~ 2 Delta/v_F, where 2 Delta is the exchange splitting.