Theories of the Glass Transition Based on Local Excitations

TL;DR

This paper reviews theories of the glass transition focusing on localized excitations and elastic interactions, proposing a framework where excitation evolution, not thermodynamic length scales, governs fragility in glass-forming liquids.

Contribution

It critically examines and compares excitation-based and elastic theories, providing a quantitative framework linking local excitations to glassy slowdown phenomena.

Findings

Elastic interactions reproduce dynamical heterogeneities quantitatively.

Excitation spectrum evolution explains activation energy without free parameters.

Local excitations govern fragility more than thermodynamic length scales.

Abstract

The dramatic slowdown of dynamics in supercooled liquids approaching the glass transition remains one of the central unresolved problems in condensed matter physics. We review approaches that attribute this slowdown to growing thermodynamic or structural length scales and discuss their difficulties in accounting for recent numerical results. These limitations motivate the present review, which critically examines alternative theories in which the glassy slowdown is instead controlled by localized excitations and their elastic interactions. After reviewing key phenomenology with a focus on the fragility of liquids, dynamical heterogeneities, thermodynamics-dynamics correlation, and the effect of kinetic rules and swap algorithms, we compare elastic descriptions based on homogeneous and local heterogeneous elasticity to excitation-based theories incorporating nonlinear responses. Results are compiled to relate global and local elastic moduli, the Debye-Waller factor, and the density of excitations, leading to a quantitative theory testable in experiments. The thermal evolution of the excitation spectrum provides a parameter-free account of the activation energy, while their elastic interactions quantitatively reproduce dynamical heterogeneities via thermal avalanche processes. Synthesized together, these results lead to a framework where the evolution of the excitation spectrum, rather than the growth of a thermodynamic length scale, governs fragility in simple glass-forming liquids -- yet mean-field concepts of dynamical transitions remain central to describing excitations and building a real-space picture of relaxation.