Theory of ground states for classical Heisenberg spin systems II

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.