  We explore the phase diagram of the five-dimensional anisotropic Abelian
Higgs model by Monte Carlo simulations. In particular, we study the transition
between the confining phase and the four dimensional layered Higgs phase. We
find that, in a certain region of the lattice parameter space, this transition
can be first order and that each layer moves into the Higgs phase independently
of the others (decoupling of layers). As the Higgs couplings vary, we find,
using mean field techniques, that this transition may probably become second
order.
