Finite temperature and confinement along the extra dimensions studied on   a five-dimensional U(1) lattice gauge model
  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 non zero 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. 
K. Farakos and S. Vrentzos