Geodesic
The Lagrange variety approach applied to frustrated classical wheels
Nanosistemy: fizika, himiâ, matematika, Tome 11 (2020) no. 1, pp. 30-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Lagrange variety approach introduced by Schmidt and Luban [J. Phys. A: Math. Gen. 36, 6351 (2003)] is applied to geometrically frustrated wheels (centered regular polygons). It is shown that the lowest energy configurations are planar or collinear. The latter one, characteristic for non-frustrated classical systems, is also observed in the presence of competing interactions in a well-determined range $(0, \alpha_c)$ of the energy function parameter $\alpha$. The ‘critical’ value $\alpha_c=1/4$ is universal, i.e., it does not depend on a system size. In this domain, the geometric frustration is present, but there is no non-trivial degeneracy.
Keywords: frustration, classical spin models, magnetic molecules, Lagrange variety. 
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W. Florek; A. Marlewski; G. Kamieniarz; M. Antkowiak. The Lagrange variety approach applied to frustrated classical wheels. Nanosistemy: fizika, himiâ, matematika, Tome 11 (2020) no. 1, pp. 30-35. http://geodesic.mathdoc.fr/item/NANO_2020_11_1_a3/