Résumé
The random-first order transition (RFOT) theory explains the slowing down of supercooled liquids with an underlying thermodynamic transition to an ideal glass phase below the experimental glass transition Tg. At the mean-field level, this transition is exactly realized and RFOT theory also predicts a first-order transition line ending at a critical point, when the overlap order parameter [1] (quantifying similarity between equilibrium liquid configurations) is linearly coupled to an external field ε. To assess the fate of mean-field results in finite dimensions, we use computer simulations to investigate the extended phase diagram (ε,T) of a 3D model supercooled liquid. Combining umbrella sampling techniques with an extensive finite-size scaling analysis, we demonstrate the existence of a first-order transition line and of a random-field Ising model critical point in the thermodynamic limit [2]. This result represents the only piece of the mean-field theory to survive other than as a crossover the introduction of finite-dimensional fluctuations.[1] B. Guiselin, G. Tarjus, L. Berthier, arXiv:2007.07625.[2] B. Guiselin, L. Berthier, G. Tarjus, Phys. Rev. E (in press).