Monte Carlo Studies of Two-Dimensional Systems with a $\theta$ Term

A $\theta$ term, which couples to topological charge, is added to the two-dimensional lattice CP^3 model and U(1) gauge theory. Monte Carlo simulations are performed and compared to strong-coupling character expansions. In certain instances, a flattening behavior occurs in the free-energy at sufficiently large $\theta$, but the effect is an artifact of the simulation methods.