Three Phases in the 3D Abelian Higgs Model with Nonlocal Gauge   Interactions
  We study the phase structure of the 3D nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by means of Monte-Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. We found that in contrast to the 3D local abelian Higgs model which has only one phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This result is quite important for studies on electron fractionalization phenomena in strongly-correlated electron systems. Implications to them are discussed. 
Shunsuke Takashima, Ikuo Ichinose, Tetsuo Matsui, and Kazuhiko   Sakakibara