Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

TL;DR

This study performs a finite-size scaling analysis of the jamming transition in two-dimensional soft disks, emphasizing the importance of corrections to scaling for accurately determining the correlation length critical exponent.

Contribution

It introduces a comprehensive finite-size scaling approach that accounts for corrections to scaling, resolving discrepancies in previous estimates of the critical exponent.

Findings

Critical exponent ν ≈ 1 determined

Corrections to scaling are essential for accurate analysis

Previous results with ν<1 are due to neglecting corrections

Abstract

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.