Thermodynamics of the Heisenberg-Ising model for | Δ | < 1 in one dimension

M. Gaudin

M. Gaudin

James D. Johnson, Barry M. McCoy, Chun-Yen Lai

H. Nencka-Ficek

Minoru Takahashi, Masuo Suzuki

The thermodynamics of the one-dimensional Heisenberg-Ising model for |Δ| ≪ 1 as well as of the X-Y-Z model is reduced to a set of non-linear integral equations under some plausible assumptions. It is remarkable that the number of unknown functions involved in them becomes finite when π/ cos -1Δ is a rational number for the Heisenberg-Ising model and when Kl /ζ is a rational number for the X-Y-Z model (where coupling constants Jx, Jy and Jz are parametrized by ζ, l, and Jz as Jx = Jz cn(2ζ, l) and Jy = Jz dn(2ζ, l); 1 ≥l ≥0, Kl ≥2ζ≥0 and Kl is the complete elliptic integral of the first kind of modulus l). The validity of our theory has been confirmed by the high-temperature expansion of the free energy through the second term for a general value of Δ and through the fourth them for Δ= ½.

Minoru Takahashi

Thermodynamic quantities such as specific heat and magnetic susceptibility are calculated numerically for the one-dimensional spin-1/2 Heisenberg-Ising model at Δ= 0, ±0.5, ±1/√2. We use a set of nonlinear integral equations which is derived from the Bethe ansatz and from some assumptions on the distribution of quasi-momenta. In the same way we calculate the specific heat of the one-dimensional X-Y-Z model in zero field, putting various values into the coupling constants (Jx, Jy, Jz).