Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids

Abstract

Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing discrepancy by incorporating critical dynamical fluctuations into a microscopic mode-coupling framework. We show that these fluctuations round off the mean-field singularity and restore ergodicity at all finite densities (or temperatures) without invoking activated dynamics or facilitation. The resulting effective theory describes the order parameter as a stochastic process with self-induced, annealed disorder, determined self-consistently at the mean-field level. In the $\beta$-relaxation regime it reduces to stochastic beta-relaxation theory, thereby unifying mode-coupling and replica-based approaches beyond mean-field. All parameters of the stochastic $\beta$-relaxation theory are fixed by the static structure, enabling parameter-free predictions that extend mean-field theory into finite dimensions.