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. *

In this paper we attempt a non-perturbative study of the five dimensional, anisotropic SU(2) gauge theory on the lattice using Monte-Carlo techniques. Our goal is the exploration of the phase diagram, define the various phases and the critical boundary lines. Three phases appear, two of them are continuations of the Strong and the Weak coupling phases of pure 4d SU(2) to non-zero coupling β ′ in the fifth transverse direction and they are separated by a crossover transition, while the third phase is a 5d Coulombic phase. We provide evidence that the phase transition between the 5D Coulomb phase and the Weak coupling phase is a second order phase transition. Assuming that this result is not altered when increasing the lattice volume we give a first estimate of the associated critical exponents. This opens the possibility for a continuum effective five dimensional field theory. *

In this article we examine the Layer phase of the five dimensional, anisotropic, Abelian gauge model. Our results are to be compared with the ones of the 4D U(1) gauge model in an attempt to verify that four dimensional physics governs the four dimensional layers. The main results are i) From the analysis of Wilson loops we verified the 1 R behavior, in the layered phase, for the potential between heavy charges. The renormalized fine structure constant in the layer phase is found to be equal to that of 4D Coulomb phase,α layer =α 4D . ii) Based on the helicity modulus analysis we show that the layers are in the Coulomb phase while the transverse bulk space is in the confining phase. We also calculated the renormalized coupling β R and found results compatible with those obtained from the Coulomb potential. Finally we calculated the potential in the 5D Coulomb phase and found 1 R 2 behavior for the static qq potential. From the study of the helicity modulus we have a possible estimate for the five dimensional renormalized fine structure constant in the region of the critical value of the bare gauge coupling . *

In this paper we study the properties of the phase diagram of a simple extra-dimensional model on the lattice at finite temperature. We consider the five-dimensional pure gauge Abelian model with anisotropic couplings which at zero temperature exhibits a new interesting phase, the layer phase. This phase is characterized by a massless photon living on the four-dimensional subspace and confinement along the extra dimension. We show that, as long as the temperature takes a nonzero value, the aforementioned layer phase disappears. It would be equivalent to assume that at finite temperature the higher-dimensional lattice model loses any feature of the layered structure due to the deconfinement which opens up the interactions between the three-dimensional subspaces at finite temperature.