Unconventional Discontinuous Transitions in Isospin Systems

We show that two-dimensional fermions with dispersion k^{2} or k^{4} 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 k^{2α} 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.