  Frustration and the associated phenomenon of "avoided criticality" have been
proposed as an explanation for the dramatic relaxation slowdown in
glass-forming liquids. To test this, we have undertaken a Monte-Carlo study of
possibly the simplest such problem, the 2-dimensional XY model with frustration
corresponding to a small flux, $f$, per plaquette. At $f=0$, there is a
Berezinskii-Kosterlitz-Thouless transition at $T^*$, but at any small but
non-zero $f$, this transition is avoided, and replaced (presumably) by a
vortex-ordering transition at much lower temperatures. We thus have studied the
evolution of the dynamics for small and moderate $f$ as the system is cooled
from above $T^*$ to below. While we do find strongly temperature dependent
slowing of the dynamics as $T$ crosses $T^*$, and that simultaneously the
dynamics becomes more complex, neither effect is anywhere nearly as dramatic as
the corresponding phenomena in glass-forming liquids. At the very least, this
implies that the properties of supercooled liquids must depend on more than
frustration and the existence of an avoided transition.
