Global Phase Diagram of Monolayer Graphene at nu=0

Graphene, a two-dimensional honeycomb lattice of Carbon atoms, has many fascinating mechanical and electronic properties. In the presence of a strong perpendicular magnetic field, it forms nearly four-fold degenerate Landau levels (with two spins and two valleys). When an integer number of these four Landau levels are filled, the system becomes a quantum Hall ferromagnet in the spin/valley space. The ordering of the ferromagnet is determined by the interactions. In this talk I will present the history of experimental and theoretical work on this problem at charge neutrality. I will end with our contribution, which considers the most general possible interactions at low energies, and provide a set of possible phase diagrams for this problem.