The high-temperature expansion of the classical Ising model with S_z^2 term

TL;DR

This paper derives a high-temperature expansion for the one-dimensional spin-S Ising model with anisotropy and magnetic field, revealing limitations of large-spin approximations at low temperatures.

Contribution

It provides a detailed high-temperature expansion up to order β^{17} for the model, including effects of anisotropy and magnetic field, and compares large-spin and spin-3 behaviors.

Findings

Thermodynamical functions are not small corrections under weak magnetic fields.

Large-spin limit models poorly approximate spin-3 functions below 35 K.

Expansion up to order β^{17} offers detailed insights into the model's thermodynamics.

Abstract

We derive the high-temperature expansion of the Helmholtz free energy up to the order \beta^{17} of the one-dimensional spin-S Ising model, with single-ion anisotropy term, in the presence of a longitudinal magnetic field. We show that the values of some thermodynamical functions for the ferromagnetic models, in the presence of a weak magnetic field, are not small corrections to their values with h=0. This model with S=3 was applied by Kishine et al. [J.-i. Kishine et al., Phys. Rev. B, 2006, 74, 224419] to analyze experimental data of the single-chain magnet [Mn (saltmen)]_2 [Ni(pac)_2 (py)_2] (PF_6)_2 for T<40 K. We show that for T<35 K the thermodynamic functions of the large-spin limit model are poor approximations to their analogous spin-3 functions.