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

Complete Density Calculations of q-State Potts and Clock Models: Reentrance of Interface Densities under Symmetry Breaking