The mechanism of jamming in soft matter was argued to be dimensionally independent in recent studies on hard spheres¹. Dimensional independence was shown by looking at the scaling exponents of jamming predicted by the infinite-dimensional mean-field hard-sphere theory developed in the last decade². These critical exponents were compared to numerical measurements in finite dimensions including 2D and 3D and were found to match surprisingly well. Such a match seemingly suggests that the infinite-dimensional theory is applicable to realistic systems.  Our current work addresses the puzzle of this lack of strong dimensional dependence usually observed in critical phenomena.

We study the jamming transition using effective inter-particle forces. 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". We observe  emergent effective many-body forces³, and quantify the amount of non-binary contributions in them as a function of  proximity to jamming. We conclude that for hard spheres the effective forces are binary precisely at jamming (and only there), similarly to the infinite-dimensional limit 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 hard⁴.

¹ For example: P. Charbonneau, J. Kurchan , G. Parisi, P. Urbani and F. Zamponi, Ann. Rev. Cond. Matt. Phys. 8 265-288 (2017).

² For example: A. Altieri , S. Franz, G. Parisi, Journal of Statistical Mechanics: Theory and Experiment, 2016 093301 (2016).

³ O. Gendelman, E. Lerner, Y.G. Pollack, I. Procaccia, C. Rainone and B. Riechers, Phys. Rev. E 94, 051001(R) (2016).

⁴ G. Parisi, Y.G. Pollack, I. Procaccia, C. Rainone and M. Singh, Submitted for publication (arXiv:1709.01607).

You can find the conference presentation at  https://goo.gl/ZXHJvi