Theory of ground states for classical Heisenberg spin systems III

TL;DR

This paper advances the understanding of classical Heisenberg spin systems by analyzing the convex Gram set of spins, identifying its symmetry group, and fully solving the ground states for the general spin triangle.

Contribution

It provides a detailed analysis of the Gram set's structure and symmetry, extending previous work and solving the general spin triangle case.

Findings

Complete solution for the ground states of the general spin triangle

Identification of the symmetry group of the Gram set

Enhanced understanding of the convex structure of spin ground states

Abstract

We extend the theory of ground states of classical Heisenberg spin systems published previously by a closer investigation of the convex Gram set of $N$ spins. This is relevant for the present purpose since the set of ground states of a given spin system corresponds to a face of Gram set. The investigation of the Gram set is facilitated by the determination of its symmetry group. The case of the general spin triangle is completely solved and illustrated by a couple of examples.