Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge   Theory
  We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED$_3$ and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition. 
Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui, Kazuhiko Sakakibara