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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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
- Heisenberg model
- planar model
- XY model
- triangular lattice
- hexagonal lattice
- ground state