Description of glass transition kinetics in 3D XY model in terms of gauge field theory

Abstract A gauge theory of the glass transition in the frustrated XY model being simplest model containing topologically nontrivial excitations is considered. Investigation of the transition kinetics of this system finds that the three-dimensional system exhibits the Vogel–Fulcher–Tammann criticality going with its freezing into a spin glass. It is analytically shown that the system demonstrates all glass transition properties, like the logarithmic relaxation, and corresponding behaviour of linear and non-linear susceptibility. The mode-coupling theory equation in the Zwanziger–Mori representation also is derived in framework of our approach. The findings provide insights into the topological origin of glass formation, that allows to make progress in understanding glass-transition processes in more intricate systems.