%0 Journal Article
%T Statistical mechanics of coupled supercooled liquids in finite dimensions
%+ Laboratoire Charles Coulomb (L2C)
%+ Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)
%A Guiselin, Benjamin
%A Berthier, Ludovic
%A Tarjus, Gilles
%< avec comité de lecture
%@ 2542-4653
%J SciPost Physics
%I SciPost Foundation
%V 12
%N 3
%P 091
%8 2022
%D 2022
%Z 2105.08946
%R 10.21468/SciPostPhys.12.3.091
%Z Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-03245252/document
%2 https://hal.science/hal-03245252/file/SciPostPhys_12_3_091.pdf
%L hal-03245252
%U https://hal.science/hal-03245252
%~ CNRS
%~ L2C
%~ LPTMC
%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ SU-SCIENCES
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021
%~ UM-EPE