Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field

We analyze a complex scalar field with phi-4 interaction and a chemical potential mu on the lattice. An exact flux representation of the partition sum is used which avoids the complex action problem and based on a generalized worm algorithm we can run Monte Carlo simulations at arbitrary densities. We study thermodynamical quantities as a function of the chemical potential mu for zero- and finite temperature. It is shown that at zero temperature thermodynamical observables are independent of mu up to a critical value mu_c (Silver Blaze phenomenon). In a spectroscopy calculation we cross-check that mu_c agrees with the mass m of the scalar field. The Silver Blaze region ends in a second order phase transition and we show that for low temperatures the second order phase boundary persists and separates a pseudo Silver Blaze region from a condensed phase with strong mu-dependence.