Multicritical behavior of the ferromagnetic Blume-Emery-Griffiths model with repulsive biquadratic couplings

Physical Review. E
A Ercule, M N Tamashiro

Abstract

The ferromagnetic (J>0) version of the Blume-Emery-Griffiths model in the region of repulsive biquadratic couplings (K<0) is considered on a Cayley tree of coordination z, reducing the statistical problem to the analysis of a two-dimensional nonlinear discrete map. In order to investigate the effect of the coordination z on the system multicritical behavior, we study the particular case K/J=-3.5 with the inclusion of crystal fields (D≠0), but vanishing external magnetic fields (H=0), for two distinct lattice coordinations (z=4 and z=6). The thermodynamic solutions on the Bethe lattice (the central region of a large Cayley tree) are associated with the attractors of the two-dimensional map. The phase diagrams display several thermodynamic phases (paramagnetic, ferromagnetic, ferrimagnetic, and staggered quadrupolar). In some cases, there are regions of numerical costability of two different attractors of the map, associated with discontinuous phase transitions between the corresponding phases. To verify the thermodynamic stability of the phases and to locate the first-order boundaries, the analytical expression of the Gibbs free energy was obtained by the method proposed by Gujrati [Phys. Rev. Lett. 74, 809 (1995)PRLTAO0031-9007...Continue Reading

References

Aug 1, 1986·Physical Review. B, Condensed Matter·M Schick, W H Shih
Dec 1, 1987·Physical Review. B, Condensed Matter·Y L WangJ D Kimel
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marco Aurélio Alves Barbosa, Vera Bohomoletz Henriques
Dec 11, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Henrique S Guidi, Vera B Henriques

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Citations

Feb 20, 2019·Physical Review. E·F O de Oliveira, M N Tamashiro
Jan 27, 2019·Langmuir : the ACS Journal of Surfaces and Colloids·F O de Oliveira, M N Tamashiro

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