Unconventional discontinuous transitions in a two-dimensional system with spin and valley degrees of freedom

We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly unconventional: The associated susceptibility diverges (or almost diverges) at the transition, yet, immediately below it, the system jumps discontinuously into a fully polarized state. We analyze the dispersion of the longitudinal and transverse collective modes in different parameter regimes above and below the transition. Additionally, we consider ordering in a system with full SU(4) symmetry and show that there is a cascade of discontinuous transitions into a set of states, which includes a quarter-metal, a half-metal, and a three-quarter metal. We compare our results with the data for biased bilayer and trilayer graphene.