Structural signatures of the unjamming transition at zero temperature

TL;DR

This paper investigates the pair correlation function in zero-temperature disordered soft-sphere packings near the jamming transition, revealing distinct structural signatures that characterize the transition.

Contribution

It identifies specific singularities and power-law behaviors in the pair correlation function that mark the unjamming transition, providing new structural insights.

Findings

First peak diverges and narrows to a delta-function at transition

Split second peak shows power-law decay and step-function drop-offs

Singularities resemble criteria used to distinguish glassy from liquid structures

Abstract

We study the pair correlation function $g(r)$ for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition is approached from the jammed side (at higher packing fraction) the first peak diverges and narrows on the small-$r$ side to a delta-function. On the high-$r$ side of this peak, $g(r)$ decays as a power-law. In the split second peak, the two subpeaks are both singular at the transition, with power-law behavior on their low-$r$ sides and step-function drop-offs on their high-$r$ sides. These singularities at the transition are reminiscent of empirical criteria that have previously been used to distinguish glassy structures from liquid ones.