  The classical ground state magnetic response of fullerene molecules that
resemble capped carbon nanotubes is calculated within the framework of the
antiferromagnetic Heisenberg model. It is found that the magnetic response
depends subtly on spatial symmetry and chirality. Clusters based on armchair
carbon nanotubes which are capped with non-neighboring pentagons and have D5d
spatial symmetry have a number of magnetization discontinuities which increases
with their size. This occurs even though the model completely lacks magnetic
anisotropy, and even though the only source of frustration are the two groups
of six pentagons located at the ends of the molecules, which become more
strongly outnumbered as the clusters are filled in the middle with more
unfrustrated hexagons with increasing size. For the cluster with 180 vertices
there are already seven magnetization and one susceptibility discontinuities.
Contrary to that, similar molecules which have D5h spatial symmetry reach a
limit of one magnetization and two susceptibility ground state discontinuities,
while fullerene molecules based on zigzag carbon nanotubes and capped by
neighboring pentagons also reach a fixed number of discontinuities with
increasing size.
