Blume-Emery-Griffiths model on the square lattice with repulsive biquadratic coupling

TL;DR

This paper applies a real-space renormalization group method to study the Blume-Emery-Griffiths model on a square lattice, accurately capturing phase transitions and phase diagrams for different signs of the biquadratic coupling.

Contribution

It introduces a symmetry-respecting renormalization group approach that accurately predicts critical parameters and explores the phase diagram for both positive and negative biquadratic couplings.

Findings

Excellent quantitative agreement with exact results for K>0.

Discovery of a rich phase diagram with antiquadrupolar and ferromagnetic phases for K<0.

Identification of continuous phase transitions without ferrimagnetic phases.

Abstract

Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K>0 are compared with other renormalization group calculations and with exact results, in order to assess the magnitude of the errors introduced by our approximate calculation. The quantitative agreement is excellent; values for critical parameters differ, in some cases, by less than 1% from exact ones. For K<0, our results lead to a rich phase diagram, with antiquadrupolar and ferromagnetic ordered phases. Contrarily to Monte Carlo simulations, these two phases meet only at zero temperature. Both antiquadrupolar-disordered and ferromagnetic-disordered transitions are found to be continuous and no ferrimagnetic phase is found.