The Coulomb-Higgs transition of the three-parameter U(1)-Higgs model
  We find a first order Coulomb--Higgs phase transition at moderately large values of the coupling $\lambda$, and no evidence for a change of order at any finite value of it. 
A. Cruz, D.Iniguez, A. Tarancon, L.A. Fernandez, A. Munoz Sudupe