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We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as T_K∝|J-J_c|^1/3 near the critical coupling J_c, and the local spin is effectively screened by a super-ohmic bath. For this class, the RKKY interaction decays spatially with a fast power law ∼1/R^7. Away from halfdoi:10.1103/physrevlett.106.016801 pmid:21231762 fatcat:zcpmtvyxpralbdhasrwzxpvwjy