Emergent Many-body Interactions Suggest Inapplicability In Practice of Hard Sphere Theory

A large effort has been devoted in the last decade to the development of an infinite-dimensional mean-field theory for the jamming transition of hard spheres[1]. The lastest studies on this topic indicate that the predictions of this theory (e.g. scaling exponents) match simulation measurements in 2D/3D suprisingly well[2], seemingly suggesting that the infinite-dimensional theory is relevant for realistic systems. Our current work addresses the puzzle of this lack of strong dimensional dependence usually observed in critical phenomena.

We use effective inter-particle forces to study the jamming transition. In thermal materials where nevertheless the mean positions are well defined on a given time-scale, these effective forces are what keeps the particles ”in place”. In continuation to a recent study in which emergence of effective many-body forces was observed[3], our current work quantifies the amount of non-binary effective interactions as a function of the closeness of jamming. We conclude that for hard spheres the effective forces are binary only at jamming, similarly to the infinite-dimensional theory and propose that this explains the match of theory and measurements. Further study of the effective forces implies that the predictions of the infinite-dimensional theory of hard spheres should be inapplicable to more realistic particles which are never absolutely hard[4].