Unconventional discontinuous transitions in isospin systems

We show that two-dimensional fermions with dispersion k² or k⁴ undergo a first-order Stoner transition to a fully spin-polarized state despite that the spin susceptibility diverges at the critical point. We extend our analysis to systems with dispersion k2α and spin and valley isospin and show that there is a cascade of instabilities into fractional-metal states with some electron bands fully depleted; narrow intermediate ranges of partially-depleted bands exist for α<1 or α > 2. The susceptibility becomes large near each transition. We discuss applications to biased bilayer and tri-layer graphene and moir\'e systems.