Discontinuous classical ground state magnetic response as an even-odd effect in higher order rotationally invariant exchange interactions

The classical ground state magnetic response of the Heisenberg model when rotationally invariant exchange interactions of integer order q>1 are added is found to be discontinuous, even though the interactions lack magnetic anisotropy. This holds even in the case of bipartite lattices which are not frustrated, as well as for the frustrated triangular lattice. The total number of discontinuities is associated with even-odd effects as it depends on the parity of q via the relative strength of the bilinear and higher order exchange interactions, and increases with q. These results demonstrate that the precise form of the microscopic interactions is important for the ground state magnetization response.