Navigating fractal canyons in glassy energy landscapes

Glass-forming systems exhibit puzzling physical and phenomenological properties, which can be directly attributed to the complex structure of their energy landscapes. In our recent study [1], we presented a modified metadynamics algorithm (MIMSE) that efficiently explores and samples low-energy regions of such high-dimensional landscapes. Further, we reported the surprising observation of canyon-like structures in such landscapes. These canyons were found to taper at lower energies and contain inherent structures (IS), that formed clusters along their floor. In this study, we use various clustering and modified dimensionality-reduction tools to study these tortuous canyons. We find strikingly similar fractal signatures for the canyons found in the landscapes of a model foam and two model glass formers - hard sphere (HS) fluids and the Kob-Andersen glass, and further, characterize them as having low effective dimensionality. For the HS glass, we use MIMSE in conjunction with systematic compression to achieve states at densities much above the jamming volume fraction, enabling us to study the canyon extremes of this landscape. Lastly, we test this algorithm on other common atomic and molecular glasses to study the presence of canyon-like structures.

[1] Amruthesh Thirumalaiswamy, Robert A. Riggleman, and John C. Crocker. Exploring canyons in glassy energy landscapes using metadynamics. Proceedings of the National Academy of Sciences, 119(43):e2210535119, 2022.