The high temperature expansion of the classical XYZ chain

The β-expansion of the Helmholtz free energy (HFE) up to order β12 of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyceʹs [Phys. Rev. Lett. 19 (1967) 581] for the XXZ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT/Jx≈0.5. The specific heat and magnetic susceptibility of the S=2 antiferromagnetic chain can be approximated by their respective classical results, within an error of 2.5%, up to kT/J≈0.8. For a vanishing external magnetic field the ferromagnetic and antiferromagnetic chains are shown to have the same classical HFE; their behaviour in a non-vanishing external magnetic field is also described.