Berezinskii-Kosterlitz-Thouless and Vogel-Fulcher-Tammann criticality in $\mathrm{XY}$ model

TL;DR

This paper develops a gauge theory to analyze the critical behavior of topological excitations in the XY model, revealing BKT criticality in 2D and Vogel-Fulcher-Tamman criticality in 3D, shedding light on spin glass formation.

Contribution

It introduces a gauge theory framework for the XY model with disorder, connecting topological excitations to different critical behaviors in 2D and 3D.

Findings

2D XY model exhibits BKT critical behavior.

3D XY model shows Vogel-Fulcher-Tamman criticality.

Insights into topological origins of spin glass formation.

Abstract

We develop a gauge theory of the critical behavior of the topological excitations-driven Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY model with weak quenched disorder. We find that while in two-dimensions the liquid of topological defects exhibits the BKT critical behavior, the three-dimensional system shows more singular Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. Our findings provide insights into the topological origin of spin glass formation.