Phase structure of U(1) lattice gauge theory by variational study with independent plaquette effective action

In order to compare independent plaquette effective action with link effective action in variational cumulant expansion, as a simple example, we calculate the plaquette internal energy Ep of U(1) LGT in three dimensions with independent plaquette effective action in variational cumulant expansion approach. The Ep-β curve is continuous, which is consistent with MC data. It shows U(1) theory has only one confined phase. It also shows the independent plaquette effective action is better than the link effective action. (orig.)