The random dipole model of weakly compensated classical impurity bands

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Abstract
The application of the random dipole model to weakly compensated classical impurity bands is reviewed, considering versions with or without a lattice. A numerical study of these systems was recently reported by Butcher, Cox and McInnes, (1984) who noted considerable disagreement between their results and predictions based on the random dipole model. To elucidate these differences the earlier theory of this model has been extended to dipoles distributed randomly on a lattice rather than on a continuum. This changes the distribution of potentials at neutral sites (identical to the density of states), particularly when the concentration of dipoles is large. The effect of allowing the dipoles to reorient in the local electric field so as to lower their energy is also considered. Using a simple pairing model of the correlation between the dipoles that this induces, it is found that the distribution of potentials is roughly halved in width, in good agreement with the numerical work. The gain in energy from the correction is also calculated; agreement here is less satisfactory, which may indicate that the distribution of potentials is a rather insensitive probe of the ordering of the dipoles.

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