Phase Transitions in lattice QED

The main objective of the work presented here is to understand the appearance of phase transitions in pure gauge and scalar lattice QED. Main results are as follows: Pure gauge compact QED with PBC shows a monopole percolation phenomena coupled to the monopole condensation. Pure gauge compact QED with Fixed Boundary Conditions (spherical topology) shows a behaviour compatible with a second order phase transition The $\gamma\to\infty$ limit of Non Compact Scalar QED with PBC is related to the Villain form of compact QED and also to the Loop Model for QED, showing a first order phase transition. Numerical a analysis of a third rank abelian Z(2) theory shows an intriguing behaviour over the phase transition that may be originated by point-like topological excitations.