Lattice Landau gauge photon propagator for 4D compact QED

In this work we report on the Landau gauge photon propagator computed for pure 4D compact QED in confined and deconfined phases large lattice volumes: ${32}^{4}$, ${48}^{4}$ ${96}^{4}$. phase, develops mass scales that render finite at all momentum no volume dependence is observed simulations performed. Furthermore, phase compatible with a Yukawa massive type functional form. For seems to approach free field as increased. both cases, also investigate static potential average value of number Dirac strings configurations $m$. gap translates into linearly growing potential, while approaches constant separations. Results shows $m$ is, least, one order magnitude larger confirm appearance connected topology group.