The Lagrange variety approach applied to frustrated classical wheels

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.