Simple argument for emergent anisotropic stress correlations in disordered solids

Abstract

It is now well-established that mechanical equilibrium in athermal disordered solids gives rise to anisotropic spatial correlations of the coarse-grained stress field1–9 that decay in space as 1/rd, 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. The presented approach bears some conceptual similarities with the field-theoretic approach of Refs. 5–7.