Permutation Symmetry Restoration in Disordered Materials

A disordered solid, such as an athermal jammed packing of soft spheres exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in three-dimensional monodisperse particle packings, we find an astonishing regularity in the distribution of basin volumes, V_Nd, as measured by their frequency of occurrence in a random sampling algorithm. Ordering the basins according to their size, from the largest at n=1, to the smallest, we find approximately that V_Nd∝ n^-1. This statistical regularity persists up to the largest systems for which we can collect sufficient data. In monodisperse packings there is "permutation symmetry" since identical particles can always be interchanged without affecting the system or its properties. Introducing any polydispersity breaks this symmetry and leads to a proliferation of distinct configurations. We present an algorithm that partially restores permutation symmetry to such polydisperse packings.