Abstract
We use a perturbative renormalization group approach with short-range continuum model interactions to analyze the competition between isotropic gapped and anisotropic gapless ordered states in bilayer graphene, commenting specifically on the role of exchange and on the importance of spin and valley flavor degeneracy. By comparing the divergences of the corresponding susceptibilities, we conclude that this approach predicts gapped states for flavor numbers $N=1,2,4$. We comment briefly on other approaches which can be used to shed light on the bilayer ground state and on the related ground state of chiral (ABC) trilayers.
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