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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.
Goodrich, C. P., Liu, A. J., & Nagel, S. R. (2012). Finite-Size Scaling at the Jamming Transition. Retrieved from https://repository.upenn.edu/physics_papers/258
Date Posted: 30 January 2013
This document has been peer reviewed.