Not yet reviewed by Pith; the record is open.

We present a method for simulating relativistic and nonrelativistic scalar field theories at finite density, with matter transforming in the fundamental representation of the global symmetry group O(N). The method avoids the problem of complex probability weights which is present in conventional path integral Monte Carlo algorithms. To verify our approach, we simulate the free and interacting relativistic U(1)=O(2) theory in 2+1 dimensions. We compute the two-point correlation function and charge density as a function of chemical potential in the free theory. At weak phi^4 coupling and zero temperature we map the m^2-mu phase diagram and compare our numerical results with perturbative calculations. Finally, we compute properties of theT-mu phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential.