Monopole percolation in scalar QED

One of the most challenging unsolved questions that arise in the application of lattice theory to particle physics is to understand the nature of the phase structure of lattice Quantum Electrodynamics. Numerical simulations of pure gauge Lattice QED with periodic boundary conditions and using the compact gauge action S = β cos θ show the existence of a first order phase transition [1]. This avoids a continuum limit for the theory. The introduction of matter fields seems not to change this behavior. Dagotto Kogut and Kocić [2] formulated a version of QED using a non compact form of the gauge term S = −βθ, i.e. keeping only the first term in the Taylor development. In this case the full theory exhibits a second order phase transition. Nevertheless, the pure gauge non-compact theory, being the action Gaussian, is simply trivial. On the other hand, it has been recognized that the monopoles play a central role in the explanation of the phase structure of lattice QED. They produce disorder and give rise of the confinement via the dual superconductor mechanism. In this sense, the gauge vacuum behaves as a magnetic