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 ϵ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature T0. We use mean-field theory to fully characterize the influence of the reference temperature T0, and we mainly study the case of a fixed, low-T0 value in computer simulations. We numerically investigate the extended phase diagram in the (ϵ, 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 ϵ 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 Tg. 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.