- Statistical mechanics of coupled supercooled liquids in finite dimensions arxiv link

Auteur(s): Guiselin B., Berthier L., Tarjus Gilles

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We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a linear coupling of amplitude $\epsilon$ 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 scaling 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 exists in the thermodynamic limit at finite temperatures. Our results show that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also establish the relevance of the physics of the RFIM for supercooled liquids, which in particular explains the qualitative difference between $2d$ and $3d$ glass-formers.