Distribution of magnon modes in dilute two-dimensional ferromagnets and antiferromagnets

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Abstract
Numerical results are reported for the distribution of magnon modes in dilute two-dimensional Heisenberg ferromagnets and antiferromagnets. The effects of site dilution and bond dilution are studied. Data on the distribution of modes in 30 × 30 arrays are compared with theoretical predictions based on the dilute-bond coherent-potential approximation of Tahir-Kheli. In the case of ferromagnets there is good qualitative aggrement over a large range of variation in the fraction of broken bonds. The situation with respect to dilute-bond antiferromagnets is less satisfactory.