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On the Wilson criterion
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 67-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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The $U(1)$-gauge theory with the Villain action is considered in a cubic lattice approximation of three- and four-dimensional tori. As the lattice spacing tends to zero, the naturally defined correlation functions converge to the correlation functions of the $\mathbf R$-gauge electrodynamics on three- and four-dimensional tori only for a special scaling, which depends on the correlation functions. Another scaling gives degenerate continuum limits. The Wilson criterion for the confinement of charged particles is fulfilled for the $\mathbf R$-gauge electrodynamics on a torus. If the radius of the initial torus tends to infinity, then the correlation functions converge to the correlation functions of the $\mathbf R$-gauge Euclidean electrodynamics. 
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Yu. M. Zinoviev. On the Wilson criterion. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 67-73. http://geodesic.mathdoc.fr/item/TMF_1999_118_1_a4/

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