Graph theory based approach to identify phase transitions in condensed matter

We put forward a methodology to identify phase transitions in condensed matter without the need to rely on any preexisting physical background. Specifically, we use graph limit theory to construct order parameters that leverage the outcomes of molecular dynamics simulations. We apply this approach to investigate the phase transitions of a Lennard-Jones system and the glass-forming ability of the Kob-Andersen binary Lennard-Jones mixture. This methodology rigorously links graph limit theory, a cutting-edge field in combinatorial mathematics, with condensed matter physics.