Thermodynamics of the limiting cases of the XXZ model without Bethe ansatz

Remarks on the convergence of the β-expansion of and s=1 Ising models

“…Consequently, those singularities in ϕ(1) (i.e., ϕ(λ = 1)) must be non-physical. We point out that a similar behavior is shown by the auxiliary function for the spin-1/2 Ising model (see reference [10]). …”

“…Nevertheless, for arbitrary values of the parameters ∆, h and D, such an approach only gives numerical solutions for the thermodynamic functions, which allow us to verify the applicability of the method presented in reference [1] to one exactly solvable limiting case of a non-integrable model [2]. The validity of the present approach has already been verified for the integrable XXZ Heisenberg spin-1/2 model [1] and its limiting cases [10].…”

The high-temperature expansion of the classical Ising model with S_{z}^{2} term

“…Figure 1 shows us that for arbitrary spin-s we can improve this approximation by recognizing that C s (1, h/|J |, D/|J |; |J |β) ≈ C s (1, 0, D/|J |; |J |β) + ∆C 1/2 (1, h/|J |, D/|J |; |J |β), at least in the region in which h/|J | ≪ 1 and |J |β 1.6. It is important to recall that the exact expression of C 1/2 (J , h, D; β) is known [14].…”

“…As a consequence of this competition, there is a perturbative effect in the AF model due to the presence of a weak magnetic field; in such regime, their thermodynamic functions F s (1, h/|J |, h/|J |; |J |β) for the spin-s model can be approximated by F s (1, h/|J |, D/|J |; |J |β) ≈ F s (1, 0, D/|J |; |J |β) + ∆F 1/2 (1, h/|J |, h/|J |; |J |β). The exact expression of the HFE of the spin-1/2 Ising model with a single-ion anisotropy term in the presence of a longitudinal magnetic field is known [14]. In the ferromagnetic model, the effect of the Zeeman coupling cannot be treated anymore as a perturbation to the interaction between first neighbors and to the single-ion anisotropy term for h/|J | 0.04.…”

The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime

“…We have compared the expansions C 7 and C 9 to the specific heat of the free spinless fermion model [14] and the spin-1/2 Ising model [17,18], both in D = 1. In order to measure the difference between each specific heat of the exactly soluble models and its expansions C 7 and C 9 , we define the percentage difference,…”