  We show that the Wang-Swendsen-Koteck\'y algorithm for antiferromagnetic
$q$-state Potts models is nonergodic at zero temperature for $q=3$ on periodic
$3m \times 3n$ lattices where $m,n$ are relatively prime. For $q \ge 4$ and/or
other lattice sizes or boundary conditions, the ergodicity at zero temperature
is an open question.
