The Lagrange variety approach applied to frustrated classical wheels
https://doi.org/10.17586/2220-8054-2020-11-1-30-35
Abstract
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.
About the Authors
W. Florek
Adam Mickiewicz University, Faculty of Physics
Poland
Poland
ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan
A. Marlewski
Poznan University of Technology, Institute of Mathematics
Poland
Poland
ul. Piotrowo 3A, 60-965 Poznan
G. Kamieniarz
Adam Mickiewicz University, Faculty of Physics
Poland
Poland
ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan
M. Antkowiak
Adam Mickiewicz University, Faculty of Physics
Poland
Poland
ul. Uniwersytetu Poznanskiego 2, 61-614 Poznan
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Review
For citations:
Florek W., Marlewski A., Kamieniarz G., Antkowiak M. The Lagrange variety approach applied to frustrated classical wheels. Nanosystems: Physics, Chemistry, Mathematics. 2020;11(1):30–35. https://doi.org/10.17586/2220-8054-2020-11-1-30-35
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