We report analytical calculations of the Helmholtz free energy of non-integrable anisotropic quantum XXZ chains in the high-temperature regime for several values of the spin S. Single-ion anisotropy and interaction with an external magnetic field are taken into account. The seven lowest-order terms in the high-temperature expansion of Helmholtz free energy are obtained. Our results contribute to the existing literature on high-temperature expansions and numerical studies of those models by discussing the effects of anisotropy upon their high-temperature thermodynamic properties, such as the average energy per site, the specific heat and magnetic susceptibility.

We derive the high-temperature expansion of the Helmholtz free energy of the quantum and classical models for the Mn(12)-ac molecule in the presence of a skew magnetic field, including the transverse term in the Hamiltonians, for [Formula: see text] K. In this region of temperature, we show that the transverse term can give a measurable contribution to the x component of the magnetization. We obtain the specific heat per site of a powder sample of Mn(12)-ac under a constant magnetic field. For strong skew magnetic fields (h/D>1), the specific heat differs up to 20% from its value of a crystal sample under purely longitudinal magnetic fields. Finally, we obtain that in the limit [Formula: see text], the values of the classical and quantum specific heat differ; in particular, for [Formula: see text] this difference is 0.96%.