Force network analysis of jammed solids

TL;DR

This paper investigates the force network in jammed solids using a model of soft particles, revealing chain-like force correlations and connecting the system to spin glass models to understand chaos and marginality.

Contribution

It introduces a novel analysis of force networks in jammed solids and maps the problem onto a Potts spin model with frustration and disorder.

Findings

Suppression of small contact angles for larger contact forces

Identification of chain-like correlations in force networks

Connection between jammed solids and spin glass models

Abstract

Using a system of repulsive, soft particles as a model for a jammed solid, we analyze its force network as characterized by the magnitude of the contact force between two particles, the local contact angle subtended between three particles, and the local coordination number. In particular, we measure the local contact angle distribution as a function of the magnitude of the local contact force. We find the suppression of small contact angles for locally larger contact forces, suggesting the existence of chain-like correlations in the locally larger contact forces. We couple this information with a coordination number-spin state mapping to arrive at a Potts spin model with frustration and correlated disorder to draw a potential connection between jammed solids (no quenched disorder) and spin glasses (quenched disorder). We use this connection to measure chaos due to marginality in the jammed system. In addition, we present the replica solution of the one-dimensional, long-range Potts glass as a potential toy building block for a jammed solid, where a sea of weakly interacting spins provide for long-range interactions along a chain-like backbone of more strongly interacting spins.