Finite-Size Scaling at the Jamming Transition

Carl P. Goodrich; Andrea J. Liu; Sidney R. Nagel

doi:10.1103/physrevlett.109.095704

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arXiv · 1204.4915

Finite-Size Scaling at the Jamming Transition

Carl P. Goodrich·Andrea J. Liu·Sidney R. Nagel

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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.

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Carl P. Goodrich, Andrea J. Liu, Sidney R. Nagel. 2012-06-06. Finite-Size Scaling at the Jamming Transition. https://doi.org/10.1103/physrevlett.109.095704

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