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 δ-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.