Ferromagnetism in one-dimensional metals: breakdown of the Hartree-Fock approximation and possible first order phase transition

Abstract

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.

8 pages, 7 figures; we have changed our choice of the ultraviolet cutoff, as suggested by a referee. Phase transition occurs now for Stoner factor smaller than unity. Fig 5 and Fig.7 are have been redrawn