  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.
