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. 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.

Shear thinning in deeply supercooled melts

“…These include the connection between the thermodynamic crisis and the diverging relaxation times (14,17,19), the length scale of the cooperative rearrangements (14), deviations from Stokes-Einstein hydrodynamics (21), aging (20), cross-over between activated and collisional transport (15,22), the cryogenic anomalies in glasses (23)(24)(25), and decoupling between momentum and charge transfer (16). Several other, distinct formalisms have yielded qualitatively similar conclusions on the liquid dynamics near the glass transition (26)(27)(28)(29)(30)(31)(32).…”

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

“…Many theoretical approaches, e.g., [15,23,24,25,26,27,14,13] have been developed over the years. The notable theory of random first order transitions (RFOT) investigates mosaics of local configurations [15,23].…”

“…Many theories of glasses rely on the hypothesis of natural structures in the glass [11,12,13,14]. Actually finding such structures in a general way has been more elusive.…”

Калибровочная Теория Перехода Жидкость - Стекло В Статическом И Динамическом Подходах

“…Система, описываемая этой моделью, фрустрирована, и ключевым ее свойством является локальная инвариантность относительно пово-ротов фрустрированных спинов [3], [8]. На локальную (калибровочную) инвари-антность рассматриваемой модели впервые обратил внимание Тулуз [9], после чего калибровочно-инвариантная теория была развита для описания спин-стекольных систем в работах [1], [3]- [5], [10], [11]. Иллюстрация локальной инвариантности фрустрированной системы приведена на рис.…”