Scalar fields at finite densities: A \delta expansion approach

We use an optimized hopping parameter expansion (linear \delta expansion) for the free energy to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector in the continuum and on the lattice at large 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.