Phase structure of U(1) lattice gauge theory with monopole term

We investigate four-dimensional compact U(1) lattice gauge theory with a monopole term added to the Wilson action. First we consider the phase structure at negative $\beta$, revealing some properties of a third phase region there, in particular the existence of a number of different states. Then our present studies concentrate on larger values of the monopole coupling $\lambda$ where the confinement-Coulomb phase transition turns out to become of second order. Performing a finite-size analysis we find that the critical exponent $\nu$ is close to, however, different from the gaussian value and that in the range considered $\nu$ increases somewhat with $\lambda$.