Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition

TL;DR

This paper investigates the scaling behavior and fluctuations of key physical observables in disordered glasses near the unjamming transition, revealing three distinct regimes and their implications for understanding material properties.

Contribution

It presents a detailed numerical analysis of contact and shear modulus fluctuations, identifying multiple scaling regimes and crossovers in low-coordination disordered sphere packings and spring networks.

Findings

Identification of three scaling regimes in disorder quantifiers

Characterization of sample-to-sample fluctuations near unjamming

Link between shear modulus fluctuations and vibrational properties

Abstract

Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance. Several such quantities are length scales ($\xi$ or $l$) that characterize the size of excitations, the decay of spatial correlations, the response to perturbations, or the effect of physical constraints in the boundary or bulk of the material. Additionally, the spatial and sample-to-sample fluctuations of macroscopic observables such as contact statistics or elastic moduli diverge approaching unjamming. Here, we discuss important connections between all of these quantities, and present numerical results that characterize the scaling properties of sample-to-sample contact and shear modulus fluctuations in ensembles of low-coordination disordered sphere packings and spring networks. Overall, we highlight three distinct scaling regimes and two crossovers in the disorder quantifiers $\chi_z$ and $\chi_\mu$ as functions of system size $N$ and proximity to unjamming $\delta z$. As we discuss, $\chi_X$ relates to the standard deviation $\sigma_X$ of the sample-to-sample distribution of the quantity $X$ (e.g. excess coordination $\delta z$ or shear modulus $\mu$) for an ensemble of systems. Importantly, $\chi_\mu$ has been linked to experimentally accessible quantities that pertain to sound attenuation and the density of vibrational states in glasses.