  We present the results of a Monte Carlo study of the three-dimensional XY
model and the three-dimensional antiferromagnetic three-state Potts model. In
both cases we compute the difference in the free energies of a system with
periodic and a system with antiperiodic boundary conditions in the
neighbourhood of the critical coupling. From the finite-size scaling behaviour
of this quantity we extract values for the critical temperature and the
critical exponent nu that are compatible with recent high statistics Monte
Carlo studies of the models. The results for the free energy difference at the
critical temperature and for the exponent nu confirm that both models belong to
the same universality class.
