Abstract
The U(1) Villain model is simulated in three and four dimensions. We locate monopoles using both the conventional DeGrand-Toussaint prescription and the exact prescription as provided by the model itself. The two monopole gases thus obtained are compared, in particular with respect to their confining and percolation properties. In this way we investigate to how strong a coupling the conventional definition of lattice monopoles remains reliable. We show that in the interesting range of "intermediate" couplings (${\ensuremath{\beta}}_{v}\ensuremath{\ge}0.3$) the difference between the two monopole gases can be very well reproduced by a random distribution of dipoles (which possesses trivial long-distance properties). This suggests that the DeGrand-Toussaint prescription can indeed be meaningfully used in studies of, for example, the U(1) phase transition and the monopole mechanism for non-Abelian confinement.
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