Avoided Phase Transitions and Glassy Dynamics In Geometrically Frustrated Systems and Non-Abelian Theories

TL;DR

This paper explores how infinitesimal non-abelian gauge backgrounds induce large degeneracies and avoid critical transitions in frustrated systems, leading to glassy dynamics and modified thermodynamics.

Contribution

It introduces a microscopic framework predicting avoided critical points and glassy behavior in systems with non-abelian gauge backgrounds, extending previous models.

Findings

Enhanced degeneracy from small non-abelian backgrounds alters thermodynamics.

Derived Vogel-Fulcher dynamics for various glass models.

Demonstrated generalized Mermin-Wagner inequality relating order parameter and relaxation times.

Abstract

We demonstrate that the application of any external uniform non-abelian gauge background, no matter how small, leads to a greatly enhanced degeneracy. This degeneracy is so large that even a non-abelian background field of infinitesimal strength leads to a shocking change in the thermodynamics. The critical temperature might be discontinuously depressed and an "avoided critical point" will emerge. Similar models were previously employed to describe the micropscopics of metallic glasses and correctly predicted the locations of the structure factor peaks. We will compare one of the fitted parameters in these plots (the magnitude of the "avoided critical temperature" for each of the supercooled liquids) and demonstrate that, on average, these might be well predicted by our microscopic picture. We find a generalized version of the Mermin-Wagner inequality which connects the magnitude of the order parameter (the absence of entropic effects) to the characteristic relaxation times present in any system. We derive Vogel-Fulcher dynamics for a multitude of glass models (including non-Abelian gauge backgrounds), and try to fortify earlier ideas suggesting avoided critical dynamics.