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 the fact 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 bi- and trilayer graphene and moiré systems.