High-temperature series expansion of the Helmholtz free energy of the quantum spin-S XYZ chain

TL;DR

This paper develops a high-temperature series expansion for the Helmholtz free energy of the quantum spin-S XYZ chain, valid for arbitrary spin and including external field and anisotropy, up to fifth order in (Jβ).

Contribution

It provides an analytic high-temperature expansion for the quantum XYZ chain valid for any spin S, extending previous results and comparing favorably with Bethe ansatz data.

Findings

Expansion agrees with Bethe ansatz results for S=1/2

Magnetic susceptibility and magnetization approximate classical results at high temperature

Expansion valid up to order (Jβ)^5

Abstract

We consider the $XYZ$ chain model of arbitrary spin $S$ in the high temperature region, with external magnetic field and single-ion anisotropy term. Our high-temperature expansion of the Helmholtz free energy is analytic in the parameters of the model for $S$, which may range from 1/2 to the classical limit of infinite spin ($S\to \infty$). Our expansion is carried out up to order $(J \beta)^5$. Our results agree with numerical results of the specific heat per site for $S=1/2$, obtained by the Bethe ansatz, with $h=0$ and D=0. Finally, we show that the magnetic susceptibility and magnetization of the quantum model can be well approximated by their classical analog in this region of temperature.