Properties of U(1) lattice gauge theory with monopole term

In 4D compact U(1) lattice gauge theory with a monopole term added to the Wilson action we first reveal some properties of a third phase region at negative $\beta$. Then at some larger values of the monopole coupling $\lambda$ by a finite-size analysis we find values of the critical exponent $\nu$ close to, however, different from the Gaussian value.