 Isotropic spin-wave vacuum energy comparison

The polarized ground state of an isotropic Heisenberg model with ferromagnetic exchange is an exact state. Its normal-ordered harmonic Hamiltonian has no pair-creation terms, no vacuum magnon occupation and no additional zero-point shift. An antiferromagnetic Néel state instead generates anomalous terms, a squeezed Bogoliubov transformation vacuum, a negative energy correction and reduced staggered magnetization. Neither statement licenses omitting normal-ordering constants from an arbitrary spin-wave model with anisotropy or a different reference state.