Mean-field-with-corrections approach to the mixed U(1) lattice gauge theory

The mixed U(1) lattice gauge theory is analyzed by the mean-field technique including $\frac{1}{d}$ corrections, $d$ being the dimension of the lattice. In order to apply the saddle-point approximation required in the method, the convenience of considering different unconstrained degrees of freedom for each power of the link variables in the action is shown. The phase diagram given by Monte Carlo simulations is reproduced with high accuracy for $d=4\mathrm{} \mathrm{and} 5$. Generalizations to other actions and gauge groups are also discussed.