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We solve numerically a set of coupled integral equations due to Halperin to obtain the spectral density of a random chain of oscillators. The results are compared with coherent-potential-approximation (CPA) and Monte Carlo calculations. The accuracy of CPA is found to be similar to that achieved in CPA calculations of the density of states: the gross features of A(q,μ) are correctly reproduced; the fine structure is averaged out. The agreement between exact and Monte Carlo calculations is excellent.
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Hirsch et al. (1977) studied this question.
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