Avoided phase transitions and glassy dynamics in geometrically frustrated systems and non-Abelian theories

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. We focus on how this arises in models previously employed to describe the microscopics of metallic glasses and correctly predicted the structure factor peaks. Some of the best fits, to date, to the dynamics of supercooled liquids were inspired by such notions for which we now provide a suggestive microscopic basis. We generalize the Mermin-Wagner inequality to high dimensions and discuss how extensive configurational entropy may be computed, by replica calculations, for a multitude of glass models (including non-Abelian gauge backgrounds). This extensive configurational entropy then allows a possible derivation of Vogel-Fulcher dynamics. We fortify earlier ideas suggesting avoided critical dynamics.