Statistical mechanics of coupled supercooled liquids in finite dimensions

TL;DR

This study explores the thermodynamic behavior of supercooled liquids in finite dimensions, revealing a first-order transition in 3D linked to RFIM universality, while 2D systems show no such transition.

Contribution

It provides a detailed finite-size analysis of coupled supercooled liquids, establishing the existence of a RFIM-like transition in 3D and its absence in 2D, linking glass physics to RFIM universality.

Findings

First-order transition line in 3D ending at RFIM critical point.

No phase transition observed in 2D systems at large sizes.

Finite-size effects align with RFIM-based predictions for supercooled liquids.

Abstract

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.