Electric-field distribution in composite media

Spatial fluctuations of the local electric field induced by a constant applied electric field in composite media are studied analytically and numerically. It is found that the density of states for the fields exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. As in solids, these singularities are generally related to saddle and inflection points in the field spectra and are useful in characterizing field fluctuations. The critical points are very prominent in dispersions with a regular, ``crystal-like,'' structure. However, they broaden and eventually disappear as the disorder increases.