Theory of ground states for classical Heisenberg spin systems II

TL;DR

This paper extends the theory of ground states in classical Heisenberg spin systems to specific finite models of the AF Kagome lattice, revealing complex ground state structures and symmetries.

Contribution

It applies the ground state theory to new finite Kagome lattice models, discovering novel three-dimensional ground states and phenomena like two-dimensional families of ground states.

Findings

Identification of three-dimensional ground states not derived from simple rotations.

Calculation of wave numbers for symmetric ground states.

Discovery of two-dimensional families of ground states in model K_{12w}.

Abstract

We apply the theory of ground states for classical, finite, Heisenberg spin systems previously published to a couple of spin systems that can be considered as finite models $K_{12},\,K_{15}$ and $K_{18}$ of the AF Kagome lattice. The model $K_{12}$ is isomorphic to the cuboctahedron. In particular, we find three-dimensional ground states that cannot be viewed as resulting from the well-known independent rotation of subsets of spin vectors. For a couple of ground states with translational symmetry we calculate the corresponding wave numbers. Finally we study the model $K_{12w}$ without boundary conditions which exhibits new phenomena as, e.~g., two-dimensional families of three-dimensional ground states.