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 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.