Finite-Size Scaling at the Jamming Transition

TL;DR

This paper investigates finite-size effects in jammed sphere packings, revealing how system size influences the jamming transition and demonstrating it as a phase transition with a critical dimension of 2.

Contribution

It provides a finite-size scaling analysis of the jamming transition, showing the breakdown of power-law scalings and identifying the upper critical dimension.

Findings

Finite-size corrections affect the contact number at jamming.

Scaling collapse reveals non-trivial scaling functions.

Jamming transition behaves as a phase transition with critical dimension 2.

Abstract

We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions, indicating an upper critical dimension of 2.