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

TL;DR

This paper introduces a new method to quantify magnetic frustration by analyzing the minimum spin dimensionality of ground states in the classical antiferromagnetic n-vector model, revealing links to geometric structures and energy limits.

Contribution

It proposes a novel approach to measure magnetic frustration through ground state dimensionality, connecting geometric configurations with spin models for arbitrary n.

Findings

Platonic and Archimedean solids have ground states with spin dimensionality equal to their spatial dimension.

Fullerene molecules and geodesic icosahedra can have ground states in up to five spin dimensions.

Frustration is also characterized by the maximum ground-state energy with variable exchange interactions.

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 $n$-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.