  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.
