Competition between frustration and spin dimensionality in the classical antiferromagnetic $n$-vector model with arbitrary $n$

Abstract

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 nn-vector model with arbitrary nn. 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 round-state energy when the exchange interactions are allowed to vary.

$\Delta$S$^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C$_{60}$: Origin and the role of symmetry

“…The response at the dimer limit provides insights into the magnetization response at least close to this limit, as has been shown for the ∆S z = 2 discontinuity close to saturation. It is highly desirable to find correlations between magnetic behavior and spatial symmetry [11,27,29,30,51,52]. In addition, and since the AHM is the large-U limit of the Hubbard model at half-filling [17,18], it is expected that the I h -symmetry fullerene molecules will share properties related to strongly-correlated models of itinerant electrons, at least for some range of their parameters.…”

“…The most symmetric fullerene molecules have icosahedral I h symmetry like C 60 . These are minimally frustrated among the fullerenes if one excludes the Platonic solid dodecahedron [23][24][25][26] that only has pentagons [27,28], and have also been found to share the ground-state magnetic response. At the classical level there are two magnetization discontinuities in an external field when all exchange interactions are equal, with the exception of the dodecahedron that has three [16,29,30].…”