Abstract
The energies and the spin configurations of the ground states of the classical Heisenberg and classical planar (XY) models with first- and second-neighbor interactions on the triangular and plane hexagonal lattices are obtained. The phase diagrams in theJ 1–J 2 plane are determined, whereJ 1 andJ 2 are the coefficients of the first- and second-neighbor interactions, respectively. It is noted for the system on the plane hexagonal lattice, that an infinite degeneracy of the ground states occurs in some region of theJ 1–J 2 plane and then the study is made under an introduction of an infinitesimal third-neighbor interaction, removing the degeneracy.
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References
M. Kaburagi and J. Kanamori,J. Appl. Phys. Suppl. 2(Pt. 2):145 (1974); Y. Tanaka and N. Uryû,J. Phys. Soc. Japan 39:825 (1975) (see Fig. 3).
T. Kudō and S. Katsura,Prog. Theor. Phys. 56:435 (1976).
A. Yoshimori,J. Phys. Soc. Japan 14:807 (1959).
D. H. Lyons and T. A. Kaplan,Phys. Rev. 120:1580 (1960); see also J. M. Luttinger, and L. Tisza,Phys. Rev. 70:954 (1946); J. M. Sanchez, D. Gratias, and D. de Fontaine,Acta Crystallogr. A 38:214 (1982).
T. Nagamiya,Solid State Physics, Vol. 20, F. Seitz and D. Turnbull, eds., p. 305, Academic Press, New York (1967).
Y. Yamamoto and T. Nagamiya,J. Phys. Soc. Japan 32:1248 (1972); T. Akino and K. Motizuki,J. Phys. Soc. Japan 31:691 (1971).
D. H. Lee, R. G. Gaflish, J. D. Joanopoulos, and F. Y. Wu,Phys. Rev. B 29:2680 (1984); D. H. Lee, J. D. Joanopoulos, J. W. Negele, and D. P. Landau,Phys. Rev. Lett. 52:433 (1984); Vik. S. Dotsenko and G. V. Uimin,Zh. Eksp. Teor. Fiz. 40:236 (1984) [Sov. Phys. JETP Lett. 40:1009 (1985)].
J. Villain,J. Phys. C 10:1717, 4793 (1977).
S. Miyashita and H. Shiba,J. Phys. Soc. Japan 53:1145 (1984).
J. Kanamori,J. Phys. Soc. Japan 53:250 (1984); M. Kaburagi, T. Tonegawa, and J. Kanamori,J. Phys. Soc. Japan 53:1971 (1984).
M. Mekata and K. Adachi,J. Phys. Soc. Japan 44:806 (1978); K. Hirakawa, H. Kadowaki, and K. Ubukoshi,J. Phys. Soc. Japan 52:1814 (1983); H. Kawamura and S. Miyashita,J. Phys. Soc. Japan 53:9 (1984); S. Fujiki, K. Shutoh, and S. Katsura,J. Phys. Soc. Japan 53:1371 (1984).
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Katsura, S., Ide, T. & Morita, T. The ground states of the classical heisenberg and planar models on the triangular and plane hexagonal lattices. J Stat Phys 42, 381–404 (1986). https://doi.org/10.1007/BF01127717
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DOI: https://doi.org/10.1007/BF01127717