Non-perturbative calculations of a global U(1) theory at finite density   and temperature
  We use an optimised hopping parameter expansion for the free energy (linear delta expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first order as the chemical potential increases. 
T.S. Evans, H.F. Jones and D. Winder