TY - JOUR

T1 - Topological anomalies in the n dependence of the n-states Potts lattice gauge theory

AU - Aizenman, Michael

AU - Fröhlich, Jürg

N1 - Funding Information:
1 A P Sloan Foundatton Fellow Work supported m part by the N.S.F grant PHY-8301493. t Mathematically speakmg, our considerations are based on some fairly elementary facts m homology theory.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1984/5/7

Y1 - 1984/5/7

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(84)90144-5

DO - 10.1016/0550-3213(84)90144-5

M3 - Article

AN - SCOPUS:1842512010

SN - 0550-3213

VL - 235

SP - 1

EP - 18

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -