Short range linear potential in 3D lattice compact QED

We study the static potential between electric charges in the finite temperature three-dimensional compact gauge theory on the lattice. We show that in the deconfinement phase at small separations between the charges the potential contains a linearly rising piece which goes over into the Coulomb potential as the distance between the charges is increased. The linear potential is due to the gas of magnetic dipoles which are realized as monopole–anti-monopole bound states.