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

TL;DR

This paper derives the exact thermodynamic properties of the ferromagnetic and staggered Blume-Emery-Griffiths model in a magnetic field, comparing it with the antiferromagnetic spin-1 Ising model at low temperatures.

Contribution

It provides the exact Helmholtz free energy and analyzes phase diagrams, ground state degeneracy, and thermodynamic behavior of the BEG model, extending previous studies to include detailed low-temperature analysis.

Findings

Magnetic field-dependent magnetization plateaux at low temperatures.

Ground state degeneracy along phase boundaries.

Equivalence of phase diagrams at T=0 for specific parameter ratios.

Abstract

We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the $z$-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at $T=0$, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in[S.M. de Souza and M.T. Thomaz, J. of Mag. and Mag. Mat. {354} (2014) 205]. We explore the implications of the equality of phase diagrams, at $T=0$, of the ferromagnetic BEG model with $\frac{K}{|J|} = -2$ and of the spin-1 AF Ising model for $\frac{D}{|J|} > \frac{1}{2}$.