High-temperature series expansion of the Helmholtz free energy of the quantum spin-SXYZchain

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 → ϱ͒. Our expansion is carried out up to order ͑J␤͒ 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.

The high temperature expansion of the classical XYZ chain

“…Joyce [2] obtained the exact solution of the classical XXZ chain, without a single-ion anisotropy term (D = 0) and in the absence of an external magnetic field (h = 0). In order to check our HTE of the classical model and to verify how it extends our previous results [5], we compare in Figs. 1a and 1b the Joyce's numerical solution for the HFE with our expansions up to orders β 5 and β 12 .…”

“…[5], we can obtain the HTE of the HFE of the classical XY Z model, up to order β 5 , by taking the limit of S → ∞ in its Eq.(3). By using the results of section 3, we obtain here the HTE of the HFE, W class , up to order β 12 , for a non-vanishing external magnetic field h and in the presence of a singleion anisotropy term in the Hamiltonian (1).…”

“…2 we compare the specific heat per site, C class (β) = −β 2 ∂ 2 ∂β 2 (βW class (β)), obtained from Joyce's solution of the classical XXZ chain (with h = 0 and D = 0) and the HTE up to β 6 (see Ref. [5]) and up to β 13 . We also include (Figs.…”

“…Recently we obtained the high temperature expansion (HTE) of the HFE of the quantum spin-S XYZ chain [5], with a single-ion anisotropy term and in the presence of an external magnetic field, up to order β 5 . (Here we have β = 1 kT , where k is the Boltzmann's constant, T is the temperature in Kelvin.)…”

“…The HFE of the classical model is obtained from Ref. [5] by taking the limit S → ∞, * Corresponding author: mtt@if.uff.br where S is the spin value (S = 1/2, 1, 3/2, 2, · · · , ∞). The calculation of this thermodynamical function of the quantum model was done by using the cummulant series for the one-dimensional models presented in Ref.…”