title: Finite-size scaling at the jamming transition.
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 nontrivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both two and three dimensions, indicating an upper critical dimension of 2.
authors.affiliation: Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Carl P
authors.initials: CP
authors.lastname: Goodrich
authors.forename: Andrea J
authors.initials: AJ
authors.lastname: Liu
authors.forename: Sidney R
authors.initials: SR
authors.lastname: Nagel