  We study a 4+1 dimensional pure Abelian Gauge model on the lattice with two
anisotropic couplings independent of each other and of the coordinates. A first
exploration of the phase diagram using mean field approximation and monte carlo
techniques has demonstrated the existence of a new phase, the so called Layer
phase, in which the forces in the 4-D subspace are Coulomb-like while in the
transverse direction (fifth dimension) the force is confining. This allows the
possibility of a gauge field localization scheme. In this work the use of
bigger lattice volumes and higher statistics confirms the existence of the
Layer phase and furthermore clarifies the issue of the phase transitions'
order. We show that the Layer phase is separated from the strongly coupled
phase by a weak first order phase transition. Also we provide evidence that the
Layer phase is separated by the five-dimensional Coulomb phase with a second
order phase transition and we give a first estimation of the critical
exponents.
