SO(N) lattice models at finite density

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 SO(N). The method avoids the problem of complex probability weights found in conventional path integral Monte Carlo algorithms. To verify our technique, we simulate the free and interacting relativistic U(1) = SO(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 the T-mu phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential