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Experimental observations of marginal criticality in granular materials

Two drastically different theories predict the marginal criticality of jamming. The full replica symmetry breaking (fullRSB) theory [1-4] predicts the power-law distributions of weak contact forces and small inter-particle gaps in infinite-dimensional hard-sphere glass, with two nontrivial exponents $θ_f=0.42311...$ and $γ=0.41269...$, respectively. While the marginal mechanical stability (MMS) analysis [5-8] predicts that the isostatic random packings of hard frictionless spheres under external stress are marginally stable and provides inequality relationships for the exponents of the weak-force and inter-particle-gap distributions. Here we measure precisely contact forces and particle positions in isotropic jammed bidisperse photoelastic disks and find the clear power-law distributions of weak forces and small inter-particle gaps, with both exponents $θ_f=0.44(2)$ and $γ= 0.43(3) $ in an excellent agreement with the fullRSB theory. As the jammed packing subject to area-conserved cyclic pure shear approaches the yielding point, the two exponents change substantially from those of the isotropic case but they still satisfy the scaling relationship provided by the MMS argument. Our results provide strong experimental evidences for the robustness of the infinite-dimensional theory and the MMS analysis in real-world amorphous materials.