In a frictionless granular packing, the stress pattern at large distances depends only on pressure fluctuations. The forces between grains are central — they push along the line connecting centers — and the stress tensor inherits this simplicity. Two-point stress correlations decay with a characteristic anisotropic form determined entirely by the pressure autocorrelation. One field controls the entire spatial structure.
Add friction, and a second field appears. Frictional grains transmit tangential forces at their contacts, generating torques. The stress tensor is no longer symmetric — it has an antisymmetric part proportional to the local torque density. Shang, Zhang, and Procaccia (arXiv:2603.08363, March 2026) show that the stress correlations in frictional amorphous solids are now governed by two independent autocorrelations: pressure and torque. And for the stress to decay in an elastic-like manner — the long-range behavior that a bulk material must exhibit — the torque fluctuations must be hyperuniform.
Hyperuniformity means that the variance of torque fluctuations in a sampling window grows more slowly than the window volume. Large-scale torque fluctuations are suppressed. This suppression is not imposed by construction or tuned by an external parameter. It is demanded by mechanical equilibrium. If pressure fluctuations are Gaussian and the material is isotropic, the only way for stress correlations to be consistent with continuum elasticity is for the torque field to self-organize into a hyperuniform state. The hidden order is a consequence of balance.
The authors validate this in experiments on two-dimensional disk packings under various loading protocols and in packings of elliptical particles, where both normal and tangential contact forces contribute to the torque. In every case, the torque variance grows sublinearly with system size — the hyperuniform signature. The disks look disordered. The force network looks random. But the torque field, measured over large enough regions, is quieter than it has any right to be.
The through-claim: friction creates a degree of freedom — torque — that mechanical equilibrium then forces into hidden order. The disorder in position and the disorder in contact forces are real. The order in torque fluctuations is also real, and it is demanded by the same equations of balance that make the material a solid. The system is disordered in every way that you can see, and ordered in the one way that the physics requires.
Shang, Zhang, and Procaccia, "Torque Hyperuniformity in Frictional Granular Matter — Theory and Experiments," arXiv:2603.08363 (March 2026).