  The three-state Potts model is numerically investigated on three-dimensional
simple cubic lattices of up to \(128^3\) volume, concentrating on the
neighborhood of the first-order phase transition separating the ordered and
disordered phases. In both phases clusters of like spins are observed with
irregular boundaries. In the ordered phase the two different non-favored spins
are found to attract each other with a long but finite range. As a result, the
neighborhoods of the non-favored spins are interpreted as domains of the
disordered phase. This explains why the first-order phase transitions
associated with the global \(Z_3\) symmetry, including the SU(3) pure-gauge
one, are so weak.
