Semiclassical and variational approximations for spin-1 magnetic chains

We discuss some refinements of semiclassical calculations for the spin-wave excitation spectrum of easy-plane ferromagnets such as CsNi${\mathrm{F}}_3$ and examine their validity for low-spin values. We also introduce a new overcomplete set of spin states, which is used to derive integral representations and variational approximations for the partition function of magnetic chains with positive uniaxial anisotropy.