### Abstract

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 Z_{n} clock and the pure SU(n) lattice gauge theories.

Original language | English (US) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Nuclear Physics, Section B |

Volume | 235 |

Issue number | 1 |

DOIs | |

State | Published - May 7 1984 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*235*(1), 1-18. https://doi.org/10.1016/0550-3213(84)90144-5