Thermodynamics of the quantum and classical Ising models with skew magnetic field

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for Jβ 0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β7 for the quantum version (spin S≥1/2) and up to order β19 for the classical version. In contrast to the S=1/2 case, the thermodynamics of the transverse Ising and that of the XY model for S>1/2 are not equivalent. Moreover, the critical line of the T=0 classical antiferromagnetic Ising model with skew magnetic field is absent from this classical model, at least in the temperature range of Jβ 0.9.