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

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  • Branco, N.S.

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.

Suggested Citation

  • Branco, N.S., 1996. "Blume-Emery-Griffiths model on the square lattice with repulsive biquadratic coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 477-486.
    • Handle: RePEc:eee:phsmap:v:232:y:1996:i:1:p:477-486
    DOI: 10.1016/0378-4371(96)00143-4
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    References listed on IDEAS

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    1. Tsallis, Constantino & Ferreira, Ricardo, 1986. "A critical phenomenon approach of biogenesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 336-348.
    2. Licia Valladares & Estela dos Santos Abreu, 1985. "Les couches moyennes, le pouvoir local et la ville. Le cas de Rio de Janeiro," Revue Tiers Monde, Programme National Persée, vol. 26(101), pages 143-153.
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