Abstract
We study the statistical mechanics of supercooled liquids when the system evolves at a temperature TT with a field \epsilonϵ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature T_0T0. We use mean-field theory to fully characterize the influence of the reference temperature T_0T0, and we mainly study the case of a fixed, low-T_0T0 value in computer simulations. We numerically investigate the extended phase diagram in the (\epsilon,T)(ϵ,T) plane of model glass-forming liquids in spatial dimensions d=2d=2 and d=3d=3, relying on umbrella sampling and reweighting techniques. For both 2d2d and 3d3d 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 \epsilonϵ ending in a critical point in the universality class of the random-field Ising model (RFIM) in d=3d=3. In d=2d=2 instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature T_gTg. 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 2d2d and 3d3d glass-formers.
Highlights
A.4 Variation of the location of the critical point with the temperature T0 of the reference configurations
Focusing on the insight that can be obtained about 3d and 2d glass-forming liquids from studying the statistical mechanics of the overlap between equilibrium and reference configurations, we have found two sets of results
The results are displayed for low values of the temperature T0 of the reference configurations, which are about or much below the extrapolated calorimetric glass transition temperature Tg
Summary
Glass formation is the direct consequence of the rapid evolution of dynamic properties of supercooled liquids as the temperature is decreased toward the experimental glass transition temperature Tg [1, 2]. They both display a first-order transition line separating the localized and delocalized phases, ending in a critical point at (εc, Tc). Recent field-theoretical calculations based on an effective description in terms of a LandauGinzburg free-energy functional of the overlap have shown that a constrained glass-forming liquid close to its putative critical point (εc, Tc) can be mapped onto a disordered system described by a φ4-theory in the presence of a random field [21,22] This shows that if the critical point survives in finite d, it should be in the universality class of the random-field Ising model (RFIM) [46]. Details on the mean-field analytical calculations are presented in an Appendix and those on the liquid models and the methods in another one
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