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(2 alpha) 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 alpha < 1 or alpha > 2. The susceptibility becomes large near each transition. We discuss applications to biased bi- and trilayer graphene and moire systems.