  We study a statistical mechanics model of two species of bosons with mutual
statistics $\theta=2\pi/n$ in (2+1) dimensions. This model realizes a
fractionalized topological phase of bosons, which is a fractionalized version
of the boson integer quantum Hall effect. The model can be studied with
sign-free Monte Carlo simulations. We study the phase transitions between the
fractionalized topological phase and a trivial insulator, and between different
topological phases. We find that these transitions are continuous, and we
measure their critical exponents.
