Numerical investigation of the equilibrium Kauzmann transition in a two-dimensional atomistic glass

Dense liquids gradually transform into nonequilibrium amorphous solids as they pass through the experimental glass transition. Experimentally, ergodicity is lost because measurements are conducted within a finite time window. More than seventy years ago, Kauzmann posed a fundamental question: If experiments could run indefinitely, would there exist a critical temperature at which an ergodicity-breaking phase transition occurs? Random first-order transitions represent the modern theoretical framework for this idea. However, theoretical calculations in finite dimensions are challenging, whereas experimental and numerical limitations on accessible timescales hinder direct observation of the putative Kauzmann transition. Here, we overcome this longstanding barrier by developing a computational strategy that properly combines three Monte Carlo methods to access the desired equilibrium thermodynamic properties of a two-dimensional atomistic glass-former down to zero temperature across a range of system sizes up to 77 particles. This enables us to directly measure thermodynamic and structural observables that provide unambiguous evidence that the system undergoes a finite-size version of the Kauzmann transition at a temperature that is much lower than other energy scales and decreases rapidly with system size, thus suggesting the existence of a zero-temperature Kauzmann transition for two-dimensional glasses. The transition is toward an ideal glass state characterized by a complex energy landscape and a hierarchical organization of low-lying states.