  An extensive investigation is given for magnetic properties and phase
transitions in one-dimensional Bethe ansatz integrable spin-1/2 attractive
fermions with polarization by means of the dressed energy formalism. An
iteration method is presented to derive higher order corrections for the ground
state energy, critical fields and magnetic properties. Numerical solutions of
the dressed energy equations confirm that the analytic expressions for these
physical quantities and resulting phase diagrams are highly accurate in the
weak and strong coupling regimes, capturing the precise nature of magnetic
effects and quantum phase transitions in one-dimensional interacting fermions
with population imbalance. Moreover, it is shown that the universality class of
linear field-dependent behaviour of the magnetization holds throughout the
whole attractive regime.
