The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β≲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...

In a recent work (J. Math. Phys. 43 (2002) 1390) we derived analytical expressions for the coefficients in the high temperature expansion of the Helmholtz free energy of periodic one-dimensional chains in the cumulant method, for arbitrary order in β. In order to do so, an auxiliary function...

Thermodynamical properties of spin-S Ising chains can nowadays be easily obtained using numerical calculation. However, from a mathematical point of view, its exact solution for arbitrary spin is still a challenge. Only limiting cases have been solved exactly, such as the infinite spin limit and...