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

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.