Magnetic behavior of a spin-1 Blume-Emery-Griffiths model

TL;DR

This paper provides an exact solution for the one-dimensional spin-1 Blume-Emery-Griffiths model with various interactions under a magnetic field, analyzing magnetic properties and the impact of biquadratic interactions.

Contribution

It offers an exact analytical solution for the 1D spin-1 BEG model with complex interactions using Green's functions, highlighting the role of biquadratic interactions.

Findings

Biquadratic interactions influence magnetization plateaus.

Exact solutions reveal temperature-dependent potentials.

Magnetic quantities vary significantly with interaction parameters.

Abstract

I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.