s=1 / 2 antiferromagnetic Heisenberg model on fullerene-type symmetry clusters

The s(i)=1/2 nearest-neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites n ranging from 24 to 32. Using the permutational and spin-inversion symmetries of the Hamiltonian, the low-energy spectrum is calculated for all the irreducible representations of the symmetry group of each cluster. Frustration and connectivity result in nontrivial low-energy properties, with the lowest excited states being singlets except for n=28. Same-hexagon and same-pentagon correlations are the most effective in the minimization of the energy, with the n=32 -D-3h symmetry cluster having an unusually strong singlet intrapentagon correlation. The magnetization in a field shows no discontinuities unlike the icosahedral I-h fullerene clusters but only plateaux with the most pronounced for n=28. The spatial symmetry as well as the connectivity of the clusters appear to be important for the determination of their magnetic properties