Origin of Corrections to Mean-field at the Onset of Unjamming

TL;DR

This paper investigates the unjamming transition in 2D frictionless disk packings, revealing a diverging length scale and deviations from mean-field predictions, with an entropic framework explaining the correlations.

Contribution

It identifies the origin of non-meanfield behavior at the unjamming transition using a static correlation function and refines the mean-field bulk-surface argument.

Findings

The PTS correlation length diverges approaching unjamming.

Deviations from mean-field predictions are characterized.

An entropic model predicts the critical boundary size.

Abstract

We present a detailed analysis of the unjamming transition in 2D frictionless disk packings using a static correlation function that has been widely used to study disordered systems. We show that this point-to-set (PTS) correlation function exhibits a dominant length scale that diverges as the unjamming transition is approached through decompression. In addition, we identify deviations from meanfield predictions, and present detailed analysis of the origin of non-meanfield behavior. A mean-field bulk-surface argument is reviewed. Corrections to this argument are identified, which lead to a change in the functional form of the critical PTS boundary size. An entropic description of the origin of the correlations is presented, and simple rigidity assumptions are shown to predict the functional form of the critical PTS boundary size as a function of the pressure.