(2 + 1)-dimensional Abelian lattice gauge theory

Abstract

A modified form of the Wilson action is studied for the Abelian field in 2 + 1 dimensions. The system is shown to be identical to the infinite-spin-component generalization of the Ising model. In the weak-coupling limit, the system factorizes into the ordinary Coulomb interaction and a new set of interactions which are a direct reflection of the compactness of the Abelian lattice field. This new interaction is divergent, for $d\le 4$, if expanded about the naive vacuum. An exact calculation shows the existence of at least two phases. A mean-field calculation shows the system to be in the same phase for all coupling $g^2$, except for $g^2=0$, where there is a phase transition.