  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 of
considerable value in the characterization of the 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.
