Description of Glass Transition kinetics in 3D XY-model in terms of Gauge Field Theory

TL;DR

This paper models the glass transition in a 3D XY-model using gauge field theory, revealing topological mechanisms behind glass formation and critical behaviors like Vogel-Fulcher-Tamman criticality.

Contribution

It introduces a gauge theory framework for the frustrated XY-model, linking topological excitations to glass transition phenomena and deriving key dynamic equations.

Findings

Demonstrates Vogel-Fulcher-Tamman criticality in the model

Shows logarithmic relaxation and susceptibility behavior

Derives mode-coupling theory equations within the approach

Abstract

We consider a gauge theory of the glass transition in the frustrated XY model being simplest model containing topologically nontrivial excitations. We describe the transition kinetics and find that the three-dimensional system exhibits the Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. We analytically show that the system demonstrates all glass transition properties, like the logarithmic relaxation, and corresponding behavior of linear and non-linear susceptibility. The mode-coupling theory equation in the Zwanziger-Mori representation also is derived in framework of our approach. Our findings provide insights into the topological origin of glass formation, that allows to make progress in understanding glass-transition processes in more intricate systems.