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Ground state magnetic response of two coupled dodecahedra

The antiferromagnetic Heisenberg model on the dodecahedron possesses a number of ground state magnetization discontinuities in a field at the classical and quantum level, even though it lacks magnetic anisotropy. Here the model is considered for two dodecahedra coupled antiferromagnetically along one of their faces, as a first step to determine the magnetic response of collections of fullerene molecules. The magnetic response is determined from the competition among the intra-, interdodecahedra exchange and magnetic field energies. At the classical level the discontinuities of the isolated dodecahedron are renormalized by the interdodecahedral coupling, while new ones show up, with the maximum number of ground state discontinuities being six for a specific range of the coupling. In the full quantum limit where the individual spin magnitude s=1/2, there are two ground state discontinuities originating in the single discontinuity of the isolated dodecahedron, and another one due to the intermolecular coupling, generating a total of three discontinuities which come one right after the other. These results show that the magnetic response of more than one dodecahedra interacting together is quite richer than the one of a single dodecahedron.