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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2020, 11 (1), P. 30–35

The Lagrange variety approach applied to frustrated classical wheels

W. Florek – Adam Mickiewicz University, Faculty of Physics, ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland; wojciech.florek@amu.edu.pl
A. Marlewski – Poznan University of Technology, Institute of Mathematics, ul. Piotrowo 3A, 60-965 Poznan, Poland
G. Kamieniarz – Adam Mickiewicz University, Faculty of Physics, ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
M. Antkowiak – Adam Mickiewicz University, Faculty of Physics, ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland

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; α_c) of the energy function parameter α. The ‘critical’ value α_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.

PACS 75.10.Hk, 75.50.Ee, 75.50.Xx, 02.40.Re

DOI 10.17586/2220-8054-2020-11-1-30-35

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