  We consider a Stoner ferromagnet in presence of a quasi-one dimensional Fermi
surface in its spin majority band. Assuming a twin $\delta$-function peaked
density of state due to the low dimensionality, we computed the single particle
self-energy. There appears an additional divergence in the self-energy and
hence in the effective mass inside the ferromagnetic phase (besides the
standard logarithmic divergence at the Stoner critical point). Since such an
effect is purely due to density of states, it might correspond to a first order
phase transition making the ferromagnetic phase into two distinct phases. This
result is in qualitative agreement with the recent specific heat capacity
measurement. We also discuss its relevance to the superconducting state in
UGe$_2$.
