MAGNONS IN THE HEISENBERG-MODEL WITH A DYNAMICAL SCALING SYMMETRY

A special Heisenberg model is considered for which the exchange integr al takes on the same value J not only for geometrically equivalent nei ghbours, but also for such j-neighbours which constitute an orbit of a ''hidden'' symmetry group of scaling transformations. The dispersion law for magnons for this model constitutes a reproduction of some rule s of arithmetic number theory. The extra symmetry is illustrated by a chain of 12 spins, which may be shown to be equivalent to a toroidal 4 x 3-periodic crystal. (C) 1998 Elsevier Science B.V. All rights reser ved.