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

Abstract

We derive the high-temperature expansion of the Helmholtz free energy up to the order β 17 of the one-

The magnetization plateaus of the ferro and anti-ferro spin-1 classical models with S2 term

“…( 1) and ( 5), we verify that the β-expansion of the HFE of this model, in terms of the parameters J, h and D in Hamiltonian (5) may be obtained by applying the following change of variables: h ′ → 2h and D ′ → 2D, in the expansion of Ref. [21] with S = 1.…”

“…The density matrix method [3] and the β-expansion of the HFE [20] have been applied to the obtainment of the exact expressions of the HFE's of the one-dimensional standard [21] and the staggered [22] spin-1 Ising models with (S z ) 2 term in the presence of a longitudinal magnetic field. The analytic expressions of these functions have been written in terms of exponentials of the parameters of the Hamiltonians (4) and (1)/ (5).…”

“…In the present work we apply the transfer matrix method [3] together with the βexpansion of the function W 1 (J, h ′ , D ′ ; β) obtained from the results of Ref. [21] with S = 1 to calculate the exact HFE of the Hamiltonian (1) in the thermodynamic limit (N → ∞), valid for T > ∼ 0. The expression of W stag 1 (J, h ′ , D ′ ; β) is obtained by using a well known result in the literature [22], namely, W stag…”

“…[20] we calculated in Ref. [21] the β-expansion of the HFE of the one-dimensional spin-S Ising model, with single-ion anisotropy term, in the presence of a longitudinal magnetic field, W S (J, h ′ , D ′ ; β), up to order β 17 , in the thermodynamic limit. The β-expansion of the HFE of the staggered Hamiltonian (4), with D ′ = 0, W stag S (J, h ′ , 0; β), was derived in Ref.…”

“…(A.8a) -(A.8c), corresponds to the eigenvalue λ 1 of matrix U, assumed to be the root with the largest modulus, we calculate the β-expansion of the functions − 1 β ln[s i ], i = 1, 2, 3, and compare each one with the expansion of the HFE of Ref. [21] with S = 1 (having made the change of variables h ′ = 2h and D ′ = 2D in the β-expansion of Ref. [21]).…”