  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. The ordered phase is found to allow admixture of disordered
domains induced by a long-range attraction acting between the two different
non-favored spins. This phenomenon gives an explanation of why the first-order
phase transitions associated with the global \(Z_3\) symmetry are so weak.
(Talk given at the International Symposium "Lattice 92" in Amsterdam, September
15-19, 1992)
