  We study the finite-temperature transition in a model XY antiferromagnet on a
pyrochlore lattice, which describes the pyrochlore material Er2Ti2O7. The
ordered magnetic structure selected by thermal fluctuations is six-fold
degenerate. Nevertheless, our classical Monte Carlo simulations show that the
critical behavior corresponds to the three-dimensional XY universality class.
We determine an additional critical exponent nu_6=0.75>nu characteristic of a
dangerously irrelevant scaling variable. Persistent thermal fluctuations in the
ordered phase are revealed in Monte Carlo simulations by the peculiar
coexistence of Bragg peaks and diffuse magnetic scattering, the feature also
observed in neutron diffraction experiments.
