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

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.

arXiv comment7 figures

References in corpus (4)

• Avoided Phase Transitions and Glassy Dynamics In Geometrically Frustrated Systems and Non-Abelian Theories
• Random Field XY Model in Three Dimensions
• Vortex glass transition in a frustrated 3D XY model with disorder
• Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model

Cited by in corpus (1)

• Spin, orbital, Weyl and other glasses in topological superfluids