Equivalence of the p-degenerate and ordinary blume-emery-griffiths models

Physical Review B - Condensed Matter and Materials Physics

Volumn 60, Issue 17, 1999, Pages 12502-12503

  Burkhardt, T ^a  

^a Temple University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954938886     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.60.12502     Document Type: Article

References (13)

1. M. Blume, V. J. Emery, and R. B. Griffiths, Phys. Rev. A 4, 1071 (1971).
2. I. D. Lawrie and S. Sarbach, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1984), Vol. 9.
3. E. Vives, T. Castán, and P. A. Lindgård, Phys. Rev. B 53, 8915 (1996).
4. D. M. Saul, M. Wortis, and D. Stauffer, Phys. Rev. B 9, 4964 (1974).
5. A. N. Berker and M. Wortis, Phys. Rev. B 14, 4946 (1976);
6. Phys. Rev. BT. W. Burkhardt and H. J. F. Knops, 15, 1602 (1977);
7. Phys. Rev. BM. Kaufman, R. B. Griffiths, J. M. Yeomans, and M. E. Fisher, 23, 3448 (1981); and references therein.
8. J. B. Collins, P. A. Rikvold, and E. T. Gawlinski, Phys. Rev. B 38, 6741 (1988), and references therein.
9. D. P. Landau and R. H. Swendsen, Phys. Rev. B 33, 7700 (1986);
10. Phys. Rev. BY. L. Wang, F. Lee, and J. D. Kimel, 36, 8945 (1987), and references therein.
11. B. Nienhuis, A. N. Berker, E. K. Riedel, and M. Schick, Phys. Rev. Lett. 43, 737 (1979).
12. The curve p=1 is probably accurate to a few percent for the square lattice, since it interpolates smoothly between four reliable points: (Formula presented) [exact result for spin-(Formula presented) Ising model], (0.422,0) [series estimate, see T. W. Burkhardt and R. H. Swendsen, Phys. Rev. B 13, 3071 (1976), and references therein], the tricritical point (0.152,0.491) [Monte Carlo renormalization-group estimate of Landau and Swendsen (Ref. 7)], and (0,(Formula presented)) [exact result for the ground-state transition].
13. The p-degenerate BEG model with disordered crystal fields has been studied by N. S. Branco and L. Bachmann, Physica A 257, 319 (1998).