Title: Zero-temperature magnetic response of small fullerene molecules at the classical and full quantum limit,
Abstract: The ground-state magnetic response of fullerene molecules with up to 36
vertices is calculated, when spins classical or with magnitude $s=\frac{1}{2}$
are located on their vertices and interact according to the nearest-neighbor
antiferromagnetic Heisenberg model. The frustrated topology, which originates
in the pentagons of the fullerenes and is enhanced by their close proximity,
leads to a significant number of classical magnetization and susceptibility
discontinuities, something not expected for a model lacking magnetic
anisotropy. This establishes the classical discontinuities as a generic feature
of fullerene molecules irrespective of their symmetry. The largest number of
discontinuities have the molecule with 26 sites, four of the magnetization and
two of the susceptibility, and an isomer with 34 sites, which has three each.
In addition, for several of the fullerenes the classical zero-field lowest
energy configuration has finite magnetization, which is unexpected for
antiferromagnetic interactions between an even number of spins and with each
spin having the same number of nearest-neighbors. The molecules come in
different symmetries and topologies and there are only a few patterns of
magnetic behavior that can be detected from such a small sample of relatively
small fullerenes. Contrary to the classical case, in the full quantum limit
$s=\frac{1}{2}$ there are no discontinuities for a subset of the molecules that
was considered. This leaves the icosahedral symmetry fullerenes as the only
ones known supporting ground-state magnetization discontinuities for
$s=\frac{1}{2}$. It is also found that a molecule with 34 sites has a
doubly-degenerate ground state when $s=\frac{1}{2}$.