Abstract
We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical results and provides a characteristic temperature for glassy dynamics that unambiguously locates the mode-coupling crossover.
Highlights
The formation of a glass from the supercooled melt results from a giant increase of the structural relaxation time when the temperature drops below the melting point [1, 2]
We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics
We found that the localization properties of unstable directions of the potential energy landscape of several models of glasses display a qualitative change close to the modecoupling crossover temperature TMCT
Summary
The formation of a glass from the supercooled melt results from a giant increase of the structural relaxation time when the temperature drops below the melting point [1, 2]. The existence of a temperature crossover separating two physical regimes of dynamic relaxation is supported by a number of empirical observations and models, but is subject to lively debates [4]. This crossover is described as an avoided dynamic singularity by mode-coupling [6] and mean-field [7] theories of glasses. Subsequent studies did not find a transition [20,21,22,23], but the transition temperature could not be crossed at equilibrium From these conflicting results it is difficult to draw firm conclusions on the nature of the mode-coupling crossover in actual three-dimensional liquids
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