String Breaking and Monopoles: a Case Study in the 3D Abelian Higgs   Model
  We study the breaking of the string spanned between test charges in the three dimensional Abelian Higgs model with compact gauge field and fundamentally charged Higgs field at zero temperature. In agreement with current expectations we demonstrate that string breaking is associated with pairing of monopoles. However, the string breaking is not accompanied by an ordinary phase transition. 
M.N. Chernodub, E.-M. Ilgenfritz, A. Schiller