Collective excitations in a planar model of a classical spin glass

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Abstract
The authors have extended earlier numerical investigations of the harmonic collective excitations in the Edwards-Anderson model (1976) of a planar spin glass to one and two dimensions. In two dimensions, as in three, low-frequency excitations propagate modes with a linear dispersion law. They outline a theoretical analysis based on the coherent potential approximation (CPA) which reproduces the spin-wave velocities that were inferred from the numerical work. In one dimension the CPA accounts for the density of states and the dynamic structure factor over the entire zone except possibly at very long wavelengths where a non-linear dispersion law is predicted.

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