  We consider planar rotors (XY spins) in $\mathbb{Z}^d$, starting from an
initial Gibbs measure and evolving with infinite-temperature stochastic
(diffusive) dynamics. At intermediate times, if the system starts at low
temperature, Gibbsianness can be lost. Due to the influence of the external
initial field, Gibbsianness can be recovered after large finite times. We prove
some results supporting this picture.
