  Randomly charged net-neutral dielectric slabs are shown to interact across a
featureless dielectric continuum with long-range electrostatic forces that
scale with the statistical variance of their quenched random charge
distribution and inversely with the distance between their bounding surfaces.
By accounting for the whole spectrum of electromagnetic field fluctuations, we
show that this long-range disorder-generated interaction extends well into the
retarded regime where higher-order Matsubara frequencies contribute
significantly. This occurs even for highly clean samples with only a trace
amount of charge disorder and shows that disorder effects can be important down
to the nano scale. As a result, the previously predicted non-monotonic behavior
for the total force between dissimilar slabs as a function of their separation
distance is substantially modified by higher-order contributions, and in almost
all cases of interest, we find that the equilibrium inter-surface separation is
shifted to substantially larger values compared to predictions based solely on
the zero-frequency component. This suggests that the ensuing non-monotonic
interaction is more easily amenable to experimental detection. The presence of
charge disorder in the intervening dielectric medium between the two slabs is
shown to lead to an additional force that can be repulsive or attractive
depending on the system parameters and can, for instance, wash out the
non-monotonic behavior of the total force when the intervening slab contains a
sufficiently large amount of disorder charges.
