  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
$\mathrm{SU(4)}$ 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 tri-layer graphene.
