najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-1-30-35najo-464Research ArticlePHYSICSФИЗИКАThe Lagrange variety approach applied to frustrated classical wheelsFlorekW.

ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan

wojciech.florek@amu.edu.plMarlewskiA.

ul. Piotrowo 3A, 60-965 Poznan

KamieniarzG.

ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan

AntkowiakM.

ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan

Adam Mickiewicz University, Faculty of PhysicsPolandPoznan University of Technology, Institute of MathematicsPoland20203107202511130–35Copyright © Florek W., Marlewski A., Kamieniarz G., Antkowiak M., 20252025Florek W., Marlewski A., Kamieniarz G., Antkowiak M.Florek W., Marlewski A., Kamieniarz G., Antkowiak M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/464

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 nonfrustrated classical systems, is also observed in the presence of competing interactions in a well-determined range (0,αc) of the energy function parameter α. The ‘critical’ value αc = 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.

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The authors declare that there are no conflicts of interest present.