Abstract
Cavity point-to-set correlations are real-space tools to detect the roughening of the free-energy landscape that accompanies the dynamical slowdown of glass-forming liquids. Measuring these correlations in model glass formers remains, however, a major computational challenge. Here, we develop a general parallel-tempering method that provides orders-of-magnitude improvement for sampling and equilibrating configurations within cavities. We apply this improved scheme to the canonical Kob-Andersen binary Lennard-Jones model for temperatures down to the mode-coupling theory crossover. Most significant improvements are noted for small cavities, which have thus far been the most difficult to study. This methodological advance also enables us to study a broader range of physical observables associated with thermodynamic fluctuations. We measure the probability distribution of overlap fluctuations in cavities, which displays a non-trivial temperature evolution. The corresponding overlap susceptibility is found to provide a robust quantitative estimate of the point-to-set length scale requiring no fitting. By resolving spatial fluctuations of the overlap in the cavity, we also obtain quantitative information about the geometry of overlap fluctuations. We can thus examine in detail how the penetration length as well as its fluctuations evolve with temperature and cavity size.