  We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo
algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at
zero temperature. We prove that this algorithm is not ergodic for symmetric
subsets of the kagome lattice with fully periodic boundary conditions: given an
initial configuration, not all configurations are accessible via Monte Carlo
steps. The same conclusion holds for single-site dynamics.
