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Multi--Layer Structure in the Strongly Coupled 5D Abelian Higgs Model

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.