Random-field Ising model criticality in glass-forming liquids

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 T_g. 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).