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

Abstract

We study in detail the exact thermodynamics of the one-dimensional standard and staggered spin-1 Ising models with a single-ion anisotropy term in the presence of a longitudinal magnetic field at low temperatures. The results are valid for the ferromagnetic and anti-ferromagnetic (AF) models and for positive and negative values of the crystal field for T > 0. Although the excited states of the ferro and anti-ferro models are highly degenerate, we show that the temperature required for reaching the first excited state in the classical spin-1 ferro model gives a scale of temperature that permits fitting the z-component of the magnetization only by the contribution of two ground states of the model. This approximation is not true for the equivalent AF function due to the fact that the AF model is gapless along the lines separating the phases in its phase diagram at T = 0. We relate the number of plateaus in the magnetization of each model to their respective phase diagrams at T = 0. The specific heat per site of the AF model distinguishes, at low temperature, the transitions A ⇋ E and G ⇋ E as the external magnetic field is varied. The exact Helmholtz free energy of the classical spin-1 model is mapped onto the equivalent function of the ionic limit of the 1D extended Hubbard model by proper transformations.

Local distributions of the 1D dilute Ising model

“…To date, exact solutions have been found for various complex models based on the 1D Ising model. They includes Blume-Emery-Griffiths model [1][2][3] , the model with localized Ising-like spins and exchanging electrons 4 , the models with single-ion anisotropy for the spin-1 chain [5][6][7] or the mixed spin-1/2 and spin-1 Ising chain [8][9][10] , the Ising-Heisenberg "decorated" chains, ladders, and tubes [11][12][13][14][15][16][17][18][19][20] and the Ising-Hubbard diamond chain and ladder 21,22 . These systems show many subtle and important phenomena, including quantized plateaux in the magnetization curves, quantum entanglement, quasi-phases and pseudo-transitions 23 , and describe the properties of real materials, such as the polymeric coordination compounds (see Refs.…”

Comparison of the ferromagnetic Blume–Emery–Griffiths model and the AF spin-1 longitudinal Ising model at low temperature

“…A analogous discussion for the spin-1 AF Ising model (see Fig.6a) has not been done in Ref. [5], though.…”

“…We also extend the discussion on the phase diagram of the spin-1 AF model in Ref. [5] in order to include the degeneracy of the ground state of the model at T = 0. Our conclusions are presented in section 5.…”

“…In the present article we study the thermodynamics of the one-dimensional BEG model in the presence of an external longitudinal magnetic field. The phase diagram of the model is discussed in detail for the ferromagnetic case, and for two different regions of the parameter K |J| , and complemented by the discussion on the phase diagram of the spin-1 AF Ising model [5].…”

“…In this appendix we follow the steps of Ref. [5], but here we write the root of cubic equation (A.4) with the largest modulus as a real number, obtaining the exact HFE of the model (2).…”