Note: Simple argument for emergent anisotropic stress correlations in disordered solids

TL;DR

This paper presents a simple geometric argument explaining the emergence of anisotropic stress correlations in disordered solids, which decay as a power law with distance, highlighting fundamental spatial stress organization.

Contribution

It introduces a straightforward, geometry-based reasoning for the scaling form of stress correlations in disordered solids, advancing theoretical understanding.

Findings

Stress correlations decay as 1/r^d in disordered solids

The argument applies across different spatial dimensions

Provides a fundamental geometric perspective on stress organization

Abstract

It is now well-established that mechanical equilibrium in athermal disordered solids gives rise to anisotropic spatial correlations of the coarse-grained stress field that decay in space as $1/r^d$, where $r$ is the distance from the origin, and $d$ denotes the spatial dimension. In this note we present a simple, geometry based argument for the scaling form of the emergent spatial correlations of the stress field in disordered solids.