Avoided criticality and slow relaxation in frustrated two-dimensional models

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 two-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 nonzero 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. Although 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.