Graphene at Very High Magnetic Fields

In the Hofstadter problem, an orbital flux of the order of a flux quantum goes through each unit cell. There are some special features when one considers a honeycomb lattice. For a certain class of hopping problems obeying a nonunitary "chiral " symmetry, when 1/q quanta of flux penetrate each unit cell, the central two bands touch at 2q Dirac points. These touchings are protected by lattice symmetries and the "chiral" symmetry. When simple short-range interactions are introduced, we find a plethora of phases which have charge,  magnetic, and/or bond order. I will compare this to Kharitonov's phase diagram in the continuum limit for tiny fields.