# Avoided criticality and slow relaxation in frustrated two dimensional models

## TL;DR

This study investigates how frustration and avoided criticality influence relaxation dynamics in a 2D XY model, revealing that these factors alone do not fully account for the dramatic slowdown observed in glass-forming liquids.

## Contribution

The paper provides a Monte Carlo analysis of the frustrated 2D XY model, showing that avoided criticality causes only moderate slowing of dynamics, challenging its role as the sole explanation for glassy behavior.

## Key findings

- Relaxation slowdown near the transition is moderate, not dramatic.
- Dynamics become more complex as temperature crosses the transition.
- Avoided criticality alone cannot explain the extreme slowdown in glass-formers.

## Abstract

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.