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 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.