Decoupling of Layers in the Three-dimensional Abelian Higgs Model

The Abelian Higgs model with anisotropic couplings in 2+1 dimensions is studied in both the compact and non-compact formulations. Decoupling of the space-like planes takes place in the extreme anisotropic limit, so charged particles and gauge fields are presumably localized within these planes. The behaviour of the model under the influence of an external magnetic field is examined in the compact case and yields further characterization of the phases.