  We study ferromagnetism in the periodic Anderson model with and without a
magnetic field by the Gutzwiller theory. We find three ferromagnetic phases: a
weak ferromagnetic phase (FM0), a half-metallic phase without Fermi surface for
the majority spin (FM1), and a ferromagnetic phase with almost completely
polarized f-electrons (FM2). The Fermi surface changes from the large
Fermi-surface in the paramagnetic state to the small Fermi-surface in FM2. We
also find that the transitions between the ferromagnetic phases can be
second-order phase transitions in spite of the absence of symmetry breaking.
While we cannot define an order parameter for such transitions in an ordinary
way, the topology of the Fermi surface characterizes the transitions, i.e.,
they are Lifshitz transitions.
