Magnetic and thermal properties of a one-dimensional spin-1 model

Abstract

We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve. In the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure

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

“…The AF model (1)/(5) is gapless for D J ≥ 1 2 along the lines h J = D J and h J = 1+ D J . We partially summarize the contents of the curves in Figs.4 by saying that the classical AF spin-1 Hamiltonian (1)/(5) is gapless along the lines that separate the phases in the diagram 1b at T = 0.The presence of plateaus in the thermodynamic functions M z of the AF Hamiltonian (1) has been reported previously by some authors [7,8,10] for positive values of D J [8]. In the following we discuss the behavior of the thermodynamic functions M z and S of the AF version of Hamiltonian (1), that is J = 1, by varying the value of the crystal field 13 per unit of J, D J , to span part of the phase diagram of the AF model (1) at T = 0 (see Fig.1b).…”

“…We can use a phenomenological approach to fit M z in the whole interval of h |J| at T < ∼ T max . We assume that the contributions to M z in the transition region of h |J| at T < ∼ T max come only from the ground states in the density matrix operator (10). We have two distinct situations to discuss.…”

“…In Ref. [10] they have extended the approach to include a biquadratic nearest-neighbour interaction term, numerically solving the coupled equations and presenting the behavior of some thermodynamic functions at low temperatures. We derived in Ref.…”

The Composite Operator Method (COM)

“…Following this procedure, one can see that there is a large class of systems (finite systems [4,9], bulk systems with interacting localized electrons [10][11][12], Ising-like systems [13][14][15][16], . .…”

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

“…(This work seems to have been neglected by the subsequent literature, though). More recently, the HFE of the S = 1 [4,5] and S = 3/2 [6] of the Ising model in the presence of an external magnetic field have been written as a set of coupled equations and solved numerically.…”