Band-filling and magnetic-field effects on the phase diagram of one-dimensional conductors

We investigate the Fermi gas model for one-dimensional (1D) conductors as a function of chemical potential and of the applied magnetic field. The bosonization method allows to prove the equivalence between these parameters, the first acting on charge degrees of freedom, the second on spin degrees of freedom. A number of results available in the literature can thus be connected. We also use the mapping to the 2D classical Coulomb gas and a two-cutoff renormalization-group method, the two energy scales being the bandwidth and the Zeeman energy (or the chemical potential). We obtain a coherent description of the Fermi gas phase diagram as a function of these two ``fields.''