Ferromagnetism in one-dimensional metals: breakdown of the Hartree-Fock   approximation and possible first order phase transition
  We calculate the Gibbs potential Gamma (M) of a one-dimensional metal at constant magnetization M to second order in the screened electron-electron interaction U. At zero temperature we find that Gamma (M) contains non-analytic corrections proportional to M^2 \ln | M| and | M |^3, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order. 
Philipp Zedler and Peter Kopietz