  All local bond-state densities are calculated for q-state Potts and clock
models in three spatial dimensions, d=3. The calculations are done by an exact
renormalization group on a hierarchical lattice, including the density
recursion relations, and simultaneously are the Migdal-Kadanoff approximation
for the cubic lattice. Reentrant behavior is found in the interface densities
under symmetry breaking, in the sense that upon lowering temperature the value
of the density first increases, then decreases to its zero value at zero
temperature. For this behavior, a physical mechanism is proposed. A contrast
between the phase transition of the two models is found, and explained by
alignment and entropy, as the number of states q goes to infinity. For the
clock models, the renormalization-group flows of up to twenty energies are
used.
