# Absence of Marginal Stability in a Structural Glass

## TL;DR

This paper investigates whether marginal stability, characterized by diverging timescales and lengthscales, exists in structural glasses, combining theoretical predictions and simulations, and finds no evidence for it in three dimensions.

## Contribution

The study challenges the mean-field prediction of a Gardner transition in structural glasses by showing the absence of marginal stability in finite dimensions through simulations.

## Key findings

- No diverging timescales or lengthscales observed in 3D simulations.
- Presence of sparse localized defects instead of marginal stability.
- Finite dimensional fluctuations significantly alter mean-field predictions.

## Abstract

Marginally stable solids have peculiar physical properties that were discovered and analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural glass-formers, combining analytical calculations in infinite dimensions to computer simulations in three dimensions. While mean-field theory predicts the existence of a Gardner phase transition towards a marginally stable glass phase at low temperatures, simulations show no hint of diverging timescales or lengthscales, but reveal instead the presence of sparse localized defects. Our results suggest that the Gardner transition is deeply affected by finite dimensional fluctuations, and raise issues about the relevance of marginal stability in structural glasses far away from jamming.