Scalar Fields at Finite Densities: a Δ Expansion Approach

We use an optimized hopping parameter expansion (linear δ-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 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. 1 Motivation In this talk we will tackle phase transitions in the U (1) or O(2) model at finite temperature and chemical potential. The work sketched out here can be found in the papers [1], [2] and builds on that set out in [3] for the case of zero temperature and zero chemical potential. We are considering the statistical partition function