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

Abstract

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 β 7 for the quantum version (spin S ≥ 1 / 2 ) and up to order β 19 for the classical version. In contrast to the S = 1 / 2 case, the thermodynamics of the transverse Ising and that of the X Y 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 | J | β ≲ 0.9 .