Jamming Criticality Revealed by Removing Localized Buckling Excitations

TL;DR

This study numerically investigates the critical behavior of jamming in sphere packings, revealing the robustness of mean-field predictions and clarifying the distribution of weak contact forces across dimensions.

Contribution

The paper introduces a criterion to distinguish localized buckling excitations in jammed packings, resolving debates on the weak force exponent and demonstrating dimensional robustness.

Findings

Mean-field marginality is dimensionally robust.

Localized buckling excitations can be separated from other particles.

The weak force exponent remains consistent across dimensions.

Abstract

Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.