Scaling collapse at the jamming transition

TL;DR

This paper investigates the critical phenomena of the jamming transition in a simple model, providing precise critical exponents and analyzing finite-size effects, supporting its universality with sphere jamming.

Contribution

It offers the first detailed numerical estimates of critical exponents for the model and analyzes finite-size scaling, confirming its universality class with sphere jamming.

Findings

Critical exponents θ ≈ 0.451 and γ ≈ 0.404 match sphere jamming.

Finite-size scaling effects are characterized in subcritical regimes.

Scaling curves are protocol-dependent but size-independent.

Abstract

The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of jamming, which is conjectured to lie in the same universality class as the jamming of spheres in all dimensions. We extract numerical estimates of the critical exponents, {\theta} = 0.451 $\pm$ 0.006 and {\gamma} = 0.404 $\pm$ 0.004, that match the exponents observed in sphere packing systems. We analyze finite-size scaling effects that manifest in a subcritical cutoff regime and size-independent, but protocol-dependent scaling curves. Our results supports the conjectured link with sphere jamming, provide more precise measurements of the critical exponents than previously reported, and shed light on the finite-size scaling behavior of continuous constraint satisfiability transitions.