  Recent discoveries in neutron scattering experiments for Kapellasite and
Herbertsmithite as well as theoretical calculations of possible spin liquid
phases have revived interest in magnetic phenomena on the kagome lattice. We
study the quantum phase diagram of the S=1/2 Heisenberg kagome model as a
function of nearest neighbor coupling J1 and second neighbor coupling J2.
Employing the pseudofermion functional renormalization group, we find four
types of magnetic quantum order (q=0 order, cuboc order, ferromagnetic order,
and Sqrt{3}x\Sqrt{3} order) as well as extended magnetically disordered regions
by which we specify the possible parameter regime for Kapellasite. In the
disordered regime J2/J1<<1, the flatness of the magnetic susceptibility at the
zone boundary which is observed for Herbertsmithite can be reconciled with the
presence of small J2>0 coupling. In particular, we analyze the dimer
susceptibilities related to different valence bond crystal (VBC) patterns,
which are strongly inhomogeneous indicating the rejection of VBC order in the
RG flow.
