We demonstrate that there is an unexpected n dependence in the topological representation of the n-states gauge Potts model as a theory of random surfaces. Our results show that there are some inherent difficulties in regarding n as a continuous parameter. In particular, we point out some difficulties in constructing plaquette percolation as the n → 1 limit of the n-states gauge Potts model and in setting up a 1/n expansion. While we find anomalies in the Wilson-loop expectation already in three dimensions, for the free energy the occur only in four or more dimensions. Related difficulties might appear in the Zn clock and the pure SU(n) lattice gauge theories.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics