The Icosahedral Symmetry Antiferromagnetic Heisenberg Model

TL;DR

This paper investigates the magnetic properties of the antiferromagnetic Heisenberg model on icosahedral fullerene clusters, revealing unconventional magnetization discontinuities due to geometric frustration, with both classical and quantum behaviors analyzed.

Contribution

It provides the first detailed analysis of magnetic discontinuities in the Heisenberg model on icosahedral fullerene clusters, highlighting the role of frustration and symmetry.

Findings

Classical magnetization shows two or three discontinuities depending on cluster size.

Quantum spin-1/2 clusters exhibit a magnetization discontinuity near saturation.

Unusual magnetic properties are consistent across different cluster sizes, indicating a generic feature.

Abstract

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 $n \leq 720$, 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 magnitudes $s_{i}={1/2}$ there is a discontinuity of quantum character close to saturation for $n \leq 80$. This common magnetic behavior indicates that it is a generic feature of $I_{h}$ fullerene clusters, irrespectively of $n$.