Abstract
The kinematics of the one-dimensional finite Heisenberg magnetic ring with impurities is discussed in the light of the general recipe of Weyl (1952). The cyclic group generating the ring, and the group of all its automorphisms, play the roles of the obvious and hidden symmetry respectively. The hidden symmetry group imposes a property of the distribution of quantum states of a translationally invariant ensemble of magnets over the finite Brillouin zone. Inhomogeneities of the distribution arise from irregular orbits of the action of the cyclic group on the set of all magnetic configurations of the ensemble. Size-dependent effects, like rarefied bands, are classified using the arithmetic structure of integers, (prime numbers, socles and arithmetic exponents), which is more appropriate than the linear order in the ring of integers.
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