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The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model isconsidered for spins sitting on the vertices of clusters with the connectivityof fullerene molecules and a number of sites $n$ ranging from 24 to 32. Usingthe permutational and spin inversion symmetries of the Hamiltonian the lowenergy spectrum is calculated for all the irreducible representations of thesymmetry group of each cluster. Frustration and connectivity result innon-trivial low energy properties, with the lowest excited states beingsinglets except for $n=28$. Same hexagon and same pentagon correlations are themost effective in the minimization of the energy, with the $n=32-D_{3h}$symmetry cluster having an unusually strong singlet intra-pentagon 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 appearto be important for the determination of their magnetic properties.Comment: Extended to include low energy spectra, correlation functions and  magnetization data of clusters up to 32 site

physical review. b, condensed matter and materials physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>antiferromagnetic Heisenberg model on fullerene-type symmetry clusters

s=12antiferromagnetic Heisenberg model on fullerene-type symmetry clusters