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We investigate the accuracy of the coherent potential approximation (CPA) fora one-dimensional array with nearest-neighbor interactions and a Gaussiandistribution of fluctuations in the on-site potential. The CPA values of theintegrated density of states and the inverse localization length are comparedwith the results of mode-counting studies carried out on arrays of 107 - 108sites. Good agreement is obtained suggesting that the CPA may be exact for thismodel. We also consider the asymptotic behavior of the inverse localizationlength and show that it can be approximated by the reciprocal of the decaylength of a state localized about a single, strongly perturbed site in anotherwise perfect lattice.

Accuracy of the coherent potential approximation for a one-dimensional array with a Gaussian distribution of fluctuations in the on-site potential