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Statistical mechanics of coupled supercooled liquids in finite dimensions

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.
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https://hal.archives-ouvertes.fr/hal-03245252
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Submitted on : Tuesday, May 31, 2022 - 11:58:12 AM
Last modification on : Friday, August 5, 2022 - 10:41:54 AM

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Benjamin Guiselin, Ludovic Berthier, Gilles Tarjus. Statistical mechanics of coupled supercooled liquids in finite dimensions. SciPost Physics, SciPost Foundation, 2022, 12 (3), pp.091. ⟨10.21468/SciPostPhys.12.3.091⟩. ⟨hal-03245252⟩

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