Abstract
We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field -spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a nontrivial universal exponent at high temperatures crossing over to a harmonic value at low temperatures. We demonstrate that this apparent evolution is controlled by a temperature-dependent population of localized glassy excitations. Our work unifies several recent lines of studies aiming at a detailed characterization of the complex potential energy landscape of glass formers, and challenges both mean-field and real space descriptions of glasses.
- Received 5 July 2021
- Revised 25 October 2021
- Accepted 2 February 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021001
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Energy landscapes have served as a visual metaphor to illustrate the physics of many complex systems with a “rugged” energy landscape, from protein foldings to molecular configurations and disordered systems. They also represent a daunting mathematical object whose geometrical properties contain relevant physical information. In glass-forming materials, the nature and properties of energy minima and of the barriers between them have been intensely studied in the past, but very little is understood about the relaxation dynamics of a given system toward energy minima. Here, we characterize this relaxation dynamics for glass-forming liquids.
Using computer simulations of a broad range of glass-forming models with different types of interactions and varying spatial dimensions—from two to eight—we fully characterize the relaxation dynamics of equilibrated glass-forming liquids toward energy minima across their rugged energy landscapes. We disentangle the universal from nonuniversal aspects of these dynamics and search for possible dynamic phase transitions as the system explores deeper parts of the landscape at lower temperatures. Our results demonstrate the limits of available mean-field and empirical analysis and reveal the role played by a population of localized glassy defects with nontrivial interactions and temperature dependence.
The steepest decent dynamics of many-body systems in complex landscapes is a timely problem, related to optimization problems and most machine-learning algorithms. Our work unifies several lines of studies aiming at a detailed characterization of the complex energy landscape of glass formers and raises several theoretical challenges regarding the nature of the glassy state in finite dimensions.
