Competing phases and their selection in two-dimensional doped Dirac and Luttinger liquid

We consider the problem of interacting spinful electrons in mono- and bilayer graphene both at zero and at finite temperature and chemical doping. Due to the many degrees of freedom, there are a plethora of available broken symmetry phases competing for nucleation. We shed light on the structure of the global phase diagrams using a set of selection rules, applicable in various strongly correlated multiband systems. We exemplify these selection rules by considering the phase diagram of the honeycomb Hubbard model.