IDENTIFYING MONOPOLES ON A LATTICE

The U(1) Villain model is simulated in three and four dimensions. We l ocate monopoles using both the conventional DeGrand-Toussaint prescrip tion and the exact prescription as provided by the model itself The tw o monopole gases thus obtained are compared, in particular with respec t to their confining and percolation properties. In this way we invest igate to how strong a coupling the conventional definition of lattice monopoles remains reliable. We show that in the interesting range of ' 'intermediate'' couplings (beta(v) greater-than-or-equal-to 0. 3) the difference between the two monopole gases can be very well reproduced by a random distribution of dipoles (which possesses trivial long-dist ance properties). This suggests that the DeGrand-Toussaint prescriptio n can indeed be meaningfully used in studies of, for example, the U(1) phase transition and the monopole mechanism for non-Abelian confineme nt.