Finite-dimensional vestige of spinodal criticality above the dynamical glass transition

TL;DR

This paper investigates finite-dimensional signatures of spinodal criticality in glass-forming liquids, revealing how critical behavior softens in lower dimensions and aligns with mean-field predictions as dimensionality increases.

Contribution

It combines numerical simulations and theoretical analysis to observe vestiges of spinodal criticality in finite-dimensional glass formers, extending understanding beyond mean-field models.

Findings

Strong softening of the mean-field singularity in 3D

Restoration of mean-field behavior above 8 dimensions

Agreement with perturbation theory across dimensions

Abstract

Finite-dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite-dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalise configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from $d=3$ to $d=9$. We observe a strong softening of the mean-field square-root singularity in $d=3$ that is progressively restored as $d$ increases above $d=8$, in surprisingly good agreement with perturbation theory.