Unconventional magnetic properties of the icosahedral symmetry antiferromagnetic Heisenberg model

The antiferromagnetic Heisenberg model on icosahedral symmetry ${I}_{h}$ fullerene clusters exhibits unconventional magnetic properties despite the lack of anisotropic interactions. At the classical level, and for number of sites $n\ensuremath{\leqslant}720$, the magnetization has two discontinuities in an external magnetic field, except from the dodecahedron where it has three, emphasizing the role of frustration introduced by the pentagons in the unusual magnetic properties. For spin magnitude ${s}_{i}=\frac{1}{2}$, there is a discontinuity of quantum character close to saturation for $n\ensuremath{\leqslant}80$. This common magnetic behavior indicates that it is a generic feature of ${I}_{h}$ fullerene clusters, irrespective of $n$.