  A new method to characterize the strength of magnetic frustration is proposed
by calculating the minimum dimensionality of the absolute ground states of the
classical nearest-neighbor antiferromagnetic $n$-vector model with arbitrary
$n$. Platonic solids in three and four dimensions and Archimedean solids have
lowest-energy configurations in a number of spin dimensions equal to their
real-space dimensionality. Fullerene molecules and geodesic icosahedra can
produce ground states in as many as five spin dimensions. Frustration is also
characterized by the maximum value of the ground-state energy when the exchange
interactions are allowed to vary.

Strongly Correlated Electrons