# Infinitesimal asphericity changes the universality of the jamming transition

## TL;DR

This paper investigates how infinitesimal asphericity in particles alters the universality class of the jamming transition, affecting critical exponents and the nature of singularities in force and gap distributions.

## Contribution

It provides a comprehensive review and new numerical evidence on how internal degrees of freedom influence the critical behavior of jamming in non-spherical particles.

## Key findings

- Infinitesimal asphericity smooths out power-law singularities in force and gap distributions.
- Critical exponents for contact number and shear modulus are derived using variational methods.
- Numerical data support the theoretical predictions about the universality class of jamming with internal degrees of freedom.

## Abstract

The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that the presence of asphericity affects the critical exponents related to the contact number and the vibrational density of states. Moreover, while the force and gap distributions of isostatic jamming present power-law behaviors, even an infinitesimal asphericity is enough to smooth out these singularities. In a recent work [PNAS 115(46), 11736], we have used a combination of marginal stability arguments and the replica method to explain these observations. We argued that systems with internal degrees of freedom, like the rotations in ellipsoids, or the variation of the radii in the case of the \textit{breathing} particles fall in the same universality class. In this paper, we review comprehensively the results about the jamming with internal degrees of freedom in addition to the translational degrees of freedom. We use a variational argument to derive the critical exponents of the contact number, shear modulus, and the characteristic frequencies of the density of states. Moreover, we present additional numerical data supporting the theoretical results, which were not shown in the previous work.