The phase structure of the non-compact abelian Higgs model

We study the non-compact abelian Higgs model on the lattice in a version with fixed-length Higgs and a Villain form of the gauge-Higgs coupling. This version permits a simplified proof of the earlier results that the model is in its Coulomb phase at sufficiently strong gauge coupling or at sufficiently small values for the Higgs length. Also, it enables us to establish the Coulomb phase simultaneously in these two regions. Similar methods demonstrate the occurrence of a phase transition to a new phase - shown previously to be the Higgs phase - valid at large Higgs length when the gauge coupling is not too strong. We use the correlation length of the Higgs field as an order parameter, and also study the behavior of the gauge propagator. (orig.)