Spin Waves in a Disordered Medium: A Simple Model with a Mobility Edge

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Abstract
A computer simulation of an isotopically disordered harmonic crystal with positive and negative masses is presented. This system may be related to a Heisenberg-Mattis random magnet, for which our results give the elementary excitations. Ideas of percolation theory are employed to explain the existence of a mobility edge in two and three dimensions whenever the positive or negative masses, but not both, percolate. For the corresponding random magnet this implies a new kind of magnon spectrum in which localized and extended states coexist.

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